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How To Use The Golden Ratio in Art Composition & Design

• Last Updated: May 9, 2024

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Want to learn the secret to balance in your art? Would you like access to a tool that geniuses from the Renaissance age implemented in their work?

There’s a formula that can help you with that. It’s been used for centuries but is still unknown to many modern artists.

Thankfully, there are some fairly easy ways you can begin incorporating this golden ratio in art to create visually stunning work.

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What is the Golden Ratio?

What are the benefits of using it, creating divine compositions in your art, how to make the golden ratio, the rule of thirds vs golden ratio in art, how to use the golden ratio in art, famous artists and artwork featuring the golden ratio, modern examples of art with the golden ratio, tools for easier implementation of the golden ratio, how will you use the golden ratio.

So, what is the golden ratio and how is it relevant to your art?

It’s an irrational number (like pi) that has some unusual properties. The ratio is 1 to 1.618 (or 1.618033988749895…) and this number is, unlike pi, a quadratic equation solution.

Wait, come back! I know math can be an intimidating (or if you’re me, downright scary) subject for many of us artists, but I promise I’m getting to the good stuff soon. This ratio is also called The Divine Proportion, phi, The Divine Section, The Fibonacci Ratio, The Golden Mean, or denoted by a phi symbol (Φ).

The sequence of seemingly random numbers is fascinating because it appears frequently throughout nature , for starters.

You will find it in shells, plants, and bone structures. Taking it a step further, you’ll find it in the reproduction patterns of rabbits . The Fibonacci sequence truly is a fascinating rabbit hole (excuse the pun) to venture down.

This ratio has been used, both intentionally and unintentionally, by designers and artists for ages. There is something intrinsically fascinating about this pattern, which manages to balance asymmetry and symmetry in a visually pleasing fashion.

The golden mean ratio can often be found depicted as a square and rectangle forming a big rectangle. This may not seem that interesting, until you realize that this sequence can be repeated perfectly and infinitely within the section.

But that’s just the beginning.

Truthfully, scientists haven’t pinned down the exact reason why the human eye is so drawn to images with the golden ratio. But it’s been proven that we like it.

Research suggests that even tiny changes that make an image closer to this ratio greatly impact the brain of the one looking at it.

The golden ratio is a powerful number present in and woven into our world. Seeing this ratio feels undeniably, intuitively right to our brains. Some believe its familiarity is what creates its beauty, as it can be found even in the human body.

But it goes even deeper than that.

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A Duke University professor, Adrian Bejan, believes that he’s figured out why we find images honoring the golden ratio so visually pleasing.

And according to him, our eyes are capable of interpreting pictures with the ratio quicker than any other type of image. Animals (including human beings) have our vision oriented horizontally.

A wild animal scans the horizon for danger, allowing him to both move faster and see better. We have evolved to do the same, and according to Bejan, shapes that are true to the golden ratio facilitate easier scanning and the transmission of images to the brain through vision.

You’re probably wondering:

How does this relate to the golden mean and how we create art?

The idea is that we will feel pleasure when our eyes find something on the horizon helpful to survival, such as shelter, a mate, or food. So seeing the golden ratio with its main subjects of interest oriented this way brings us pleasure through its beauty.

How can you begin using this magical ratio in your artwork to create compelling pieces ? If the idea of using math sounds like a stifling idea to you, you may find it helpful to consider it a general guideline.

A general rule or theme to create from can lend you more freedom in your pieces as the guesswork of placement and proportions will be minimized.

Think of this as a useful tool instead of a strict rule. In fact, you might even use it already without knowing it! Basically, the golden ratio can be used to choose the placement and size of your art’s content, whether it’s a website you’re designing or a digital character piece.

How exactly is this done?

You can choose the general size of the piece’s layout using the golden rectangle, place focal points where the golden spiral would go, or use a combination of all techniques.

We will give you some specific examples (in photography, web design, and more) to gain inspiration from in a bit. But for now, let’s start with the basics; creating a golden rectangle that can be used as a simple base for your work.

Here’s the deal:

If you want to use the golden ratio art, your first choice will be which shape to focus on. The most familiar shape associated with the golden ratio is the rectangle. And the most visually appealing rectangles are golden rectangles.

How to Construct a Golden Rectangle

To use the golden rectangle for your art, just follow these simple steps:

• Make a 1×1 square. This will be the smallest square on your canvas.
• Create another equal size square to the right of the original square.
• Create a 2×2 square under your original two 1×1 squares.
• Now create a 3×3 square to the left of the first three squares.
• Lastly, create a 5×5 square that goes above this group of squares.

You just successfully made a golden rectangle using the golden ratio. ​ Learning more about how this works can offer you extra inspiration, if you’re the rare artistic type who likes to think about numbers.

If you prefer simplicity, we’ll give you some tools that will make it easier later in the article.

Using the Golden Ratio with Circles

For most artistic purposes, the golden rectangle will be easiest and most useful, but that’s far from all you can use the golden ratio for.

It’s also possible to use circles in a similar way. You can make a golden ratio using circles instead of squares. If you want to be precise about it, it may be easiest to start with the squares and then fill in the circles.

It’s even possible to make a golden triangle spiral, which we will get to in a moment.

Using Golden Triangles

If you’re working with a composition using diagonal lines, you can use golden triangles to create more visually appealing art. This involves a series of triangles with the same shape. You can place your subjects of interest inside these triangles to create a balanced piece of art.

For example, create a mountain scape where the size of each mountain roughly corresponds with the sizes of the triangles here:

Alternatively, you can create a golden spiral shape using triangles.

For this you’d use an isosceles triangle (a shape with one distinctive side and two equal sides, creating a golden proportion). You could then put these triangles together to create the spiral shape.

More on this later.

How To Create The Phi Grid

You can use a grid based on the golden ratio to ensure your illustrations, logos, or images are visually sound. A grid is a good way to find minor adjustments in subject placement that you need to make or to find a good guide for where to crop.

It’s just a generally helpful strategy for a more organized finished product. The Altrise Golden Section Grid Software is one option for implementing the phi grid in your work.

Where Can You Find The Golden Ratio?

The golden ratio is present throughout the world in design, the human body, nature, photography, art, and more. It seems to be nature’s favorite equation.

Actually, when you start looking for it, you might have a hard time un-seeing it. Here are some examples:

The golden ratio has been used for centuries and is no stranger to High Renaissance art. For instance, it appears over two dozen times in the famous Sistine Chapel alone. We will cover some specific examples from this later.

Architecture

The Fibonacci sequence has been used for ages in architecture. The golden ratio appears in the Great Pyramid of Egypt.

The Parthenon in Greece is another famous example of the ratio and features a rectangle true to golden proportion.

The golden mean can also be found in various designs and logos, including the iCloud logo . There is also rumor that the Apple symbol was designed with the ratio.

Faces are considered more attractive if they are in proportion and somewhat symmetrical, like the golden ratio. A study done in 2009 found the ideal ratios for attractiveness.

Photography

Visual creators, such as photographers, often incorporate the golden mean into their projects. One common way to do this is positioning the focal point of a photograph where the golden spiral’s curl would be.

You won’t have to look far to find the golden ratio in nature . The Fibonacci spiral can often be found in the heads of flowers, the formation of petals, and shells.

Pine cones are another good example of this phenomenon, along with this absolutely crazy-looking broccoli.

The beauty of this broccoli is undeniable. And your art can be just as beautiful if you learn how to use the golden mean correctly!

But first, let’s start with a guideline you might be a little more familiar with using.

The way you crop and frame images has a large impact on how the viewer feels about your art, even if they aren’t aware of it.

This section will cover two different ways to structure images to make them more visually appealing and engaging.

The Rule Of Thirds

The rule of thirds is a simple, common composition rule that photographers have been using for ages. This guideline involves envisioning two sets of parallel lines running perpendicular to each other.

The end result is nine equal-sized boxes across the canvas or layout and four intersecting points. These points are “sweet spots” where it’s best to place subjects of focus, illustrated by the green spots below.

The bottom line is:

Our brains like efficiency, so when the eye can easily focus on the composition subject without having to search, it’s satisfying. The rule of thirds offers a good solution for this.

• Gives your image equal weighting and visual harmony.
• It’s easy to implement due to its symmetry.
• You have a lot of choice with “sweet spots” to place subjects.

• May come across as too divided, depending on your subject matter.
• The forced symmetry can feel too perfect and not organic enough.

The Golden Ratio

Applying the golden ratio to art means placing the main subjects along intersecting lines, as you’d do when using the rule of thirds.

The “phi grid” is similar to the rule-of-thirds layout but the parallel lines are closer to the center. This results in nine boxes that are not uniform in size.

• The top section of the grid is perfect for landscape pieces.
• The grid divides space on the canvas mathematically.
• Works well for images where weight should be toward the frame’s outer edges.

• The phi grid can be harder to create than the rule-of-thirds grid.
• It may leave awkward blank spaces in your work, if you aren’t careful.

The golden ratio is harder to implement than the rule-of-thirds grid, so why bother?

Well, the phi grid allows you to work with the sweeping arc of the Fibonacci spiral.

When you place your subjects of focus along this curved line, you are drawing your viewers’ eyes to the spiral coil. It’s like a subliminal sign showing them where to look.

We all recognize when a piece of art has “it.” You can’t stop staring at the image, it seems perfectly balanced and just feels right. This is what the golden ratio can do.

And using the Golden Ratio in your art is simpler than you might think. There are a couple of quick tricks you can use to insert it into your layouts, or you can plan a little more to fully embrace the concept and have quick access to better composition and all-around balanced and beautiful art.

This can be used as a general idea to keep in mind (for instance, visualizing the golden spiral to see if your main point of focus aligns with it) or something more precise.

What follows are some techniques for art that is balanced based on the golden ratio. Use these on your drawing tablet , for traditional oil painting , or even for designing your website.

Using Points of Interest

Any rectangle or square (especially ones that use the golden ratio) have areas inside that are visually appealing. This is where you could place a tree in a landscape painting, or someone’s face in a portrait-style piece.

You can find these points by:

• Drawing a line from the top corner to the opposite bottom corner on both sides, making an “X” shape in the middle.
• From the middle of the “X” to each corner, mark the midway point. The red dots below indicate where the midway points would be. These are the “eyes” of the golden rectangle.

Place any items near or within these focal points to draw attention to the subjects of your art pieces.

Applying The Ratio To Photography

The golden ratio can be used as a sizing guide in photo editing. The simplest way to use the ratio in your design is to crop your images down to form a golden rectangle.

This won’t be suitable for every photo you take, but it’s a helpful guideline.

You can find a variety of tools that will help with this online and in our tools section later in the article.If you crop your image to create a golden rectangle, you can take it a step further by guiding the shot to reflect the golden spiral, too.

And with these simple steps, you’ve just doubled down on your art-composition-balancing!

When deciding where to crop, you can visualize the photo with golden proportions with the main subject of the picture in the place that the golden spiral center would be.

This is a simple, natural way to add interest to your work and can apply not just to photo editing, but general graphic design.

The triangles may be a bit harder to use than the phi grid or golden rectangle as creating a perfect triangle may require a little more math.

If you are working with a piece that has a lot of diagonal lines and want to know how to balance subject matter in it, this is a great guide.

Using the Golden Spiral in Art

For those wondering how to use the golden ratio in their composition, the spiral shape is another option for a more balanced piece.

Making use of this trick can mean the difference between a forgettable piece of art and a visually stunning masterpiece that pauses people in their tracks.

In your paintings and drawings (digital or traditional), there should always be something drawing the viewer’s eye to the composition’s center. This can be several subjects or a line.

The golden mean used as a spiral can be visualized as squares and rectangles. This would be a golden rectangle divided by the ratio leading to a series of progressively smaller squares and rectangles.

This framework can help you decide where to place subjects inside the frame. The most important focal points should go in the smaller rectangles.

Adobe Lightroom has a variety of crop overlays you can use including one named the “Golden Spiral.”

Implementing The Golden Ratio In Web Design

You can also implement the Fibonacci sequence to make your digital designs more appealing.

If you are designing the layout of a webpage, for instance, you would arrange the sidebar and content so that it’s true to the 1:1.61 ratio. This can be rounded down or up by a point or so and will still work well.

The rectangle spiral can also be a useful guide for where to place text and how large to make it, leading to eye-catching designs and calling attention to the place it matters most.

The Golden Ratio In Logo Design

The Fibonacci sequence can also be used to create more engaging, visually appealing logos for your business .

Viewers will be drawn to the golden ratio of the design and find it much more memorable and appealing, even if they aren’t sure why.

The artistic masters of history were onto to this magical ratio, which could explain (at least partially) their brilliance.

Let’s look at some famous examples to illustrate this:

Leonardo Da Vinci

“The Last Supper” by Da Vinci clearly illustrates multiple uses of the Divine Proportion. Painted at the end of the 15th century, various architectural and design features display clear golden ratios.

The figures in the painting all appear right below the line that marks the ratio. And if you look closely, it even seems as though the disciples in the image were placed around Jesus in divine proportions.

From the way he centered Jesus in the painting, to the height of the figures on his left against the distance between table and ceiling, it’s clear that Da Vinci drew much inspiration from the Fibonacci sequence.

Right around the same time he created that masterpiece, Da Vinci was responsible for illustrations in a book titled “The Divine Proportion” (De Divina Proportione). The book discusses artistic and mathematical proportion and how the golden ratio is applied to architecture and art aesthetics .

Michelangelo

You may be familiar with Michelangelo’s “Creation of Adam” painting on the Sistine Chapel’s ceiling.

At first glance, it may not seem obvious that he used mathematics in this masterpiece. If you look a little closer at the segment featuring God and Adam, though, you’ll see that God’s finger is touching Adam’s finger right where a divide exists in the golden ratio.

So, it turns out that the harmony and beauty that Michelangelo was so famous for wasn’t only based on his knowledge of human anatomy.

He may have also known that structures in anatomy feature the golden ratio and used this knowledge to enhance his paintings.

One of the most famous pieces by Raphael is “ The School of Athens ” in the Vatican, considered by many to be his masterpiece.

This is a perfect example of the golden ratio in Renaissance art. Painted in the early 1500s, the image was part of his commission to decorate the Stanze di Raffaello.

The golden ratios can be found throughout this composition. See if you can spot them.

Other examples of the golden proportion in art are “The Sacrament of the Last Supper” by Dali and The Mona Lisa.

It wasn’t just the classic Italian masters who made use of the divine proportion. Here are a few modern artists implementing the Fibonacci sequence in their work today.

Stephen Silver

Stephen Silver is an art teacher and character designer with work featured on Nickelodeon Animation, Sony Feature Animation, and Disney Television.

Among others, he created “Danny Phantom” and “Kim Possible” and also owns an art school in California. He has talked openly about using the golden ratio in his composition and design.

Silver describes the divine proportion as flawless and brilliant because it offers “small, medium, and large” parts of objects and characters.

He states, “That’s what we really build design on, because we’re so used to seeing it in the human face and everywhere we look in trees and animals.”

Ralph McQuarrie

Sci-fi is a beloved genre for digital artists everywhere. Both literally and figuratively, if it wasn’t for Ralph McQuarrie, Star Wars would not exist as we know it. And what kind of world would that be?!

George Lucas got in touch with McQuarrie for help visualizing the characters, vehicles, and planets he envisioned for his story.

Darth Vader might be the most well-known villain in the history of film, but what if there’s something specific that we find so intriguing about his costumes and helmet? Can you spot any golden proportions in this photo?

Mark Mayers

Freelance designer and illustrator Mark Mayers has almost two decades of experience with art. He writes tutorials, has won awards for his artwork, and has openly discussed using the Fibonacci sequence in his game design!

There is definitely something innately pleasing in the way he created the visuals for one specific game.

DESOLUS is a first-person puzzle game about a surreal world in between dimensions. Mark Mayers started creating this game in 2014. Can you spot his use of the golden mean in this teaser?

These are just a few artists who apply the Fibonacci sequence to their work. If you start looking, you’ll probably find many golden ratio examples in art to draw inspiration from.

If you are still shuddering at the thought of trying to use math in your art, you can take the guesswork out of the equation by using tools specifically created for the task.

If digital art is your main game, this software can be used to enhance your work or check that it’s true to the golden ratio. It’s a transparent grid for Mac and Windows that can be applied to whatever other creation software you’re using.

PhiMatrix includes spirals, diagonals, and grids, while the 1.618 Pro version comes with more patterns. The program allows you to choose a template, resize it as you see fit, or use it as a base to create a piece from.

You can try it for two weeks on Windows or on Mac for free before deciding whether to continue with it.

Golden Mean Calipers

If you prefer to draw or paint the traditional way, Golden Mean Calipers can help you check composition, create balance, and construct perfect layouts.

This unique tool can be used to create mathematically sound golden proportions to fill in later, or just to check the proportions of an existing design.

These are especially useful if you’re creating art related to body dimensions and anatomy. The caliper arms close and open to measure various distances, while keeping the distances at 1:1618.

The dimensions are 1.5 to 12.8 inches for a range of options and the calipers come in a durable holder.

The Golden Ratio Calculator

This is a quick and simple tool for finding the golden ratio in a specific number.

If you need to calculate layout measurements regularly in your developing or design work, the Golden Ratio Calculator can be helpful. The numbers are rounded 2 decimal places, so it’s pretty accurate.

The app works with most Android tablets and has no ads (because who wants their creative process disrupted by those?). It works quickly and is pretty easy to use.

This can also be used when you’re selecting your canvas size in whatever drawing software you’re using to ensure the rectangle is of golden proportions.

Whether you’re a web designer, traditional painter, or have a knack for photo editing, the Fibonacci spiral is your friend. It can be as simple or as complicated as you want it to be, but I like the idea of using a combination of golden-ratio-related tricks in my art.

Has this article given you some ideas for how to start implementing the golden mean in your work? If so, comment with your ideas. Also feel free to leave any other questions or thoughts you have on the topic and thanks for reading!

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An introduction to the golden ratio.

One of the most famous ratios in mathematics and design goes all the way back to the ancient Greeks. Learn more about the golden ratio and its role in art and design.  

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What is the golden ratio?

The golden ratio, also known as the golden number, golden proportion, or the divine proportion, is a ratio between two numbers that equals approximately 1.618. Usually written as the Greek letter phi, it is strongly associated with the Fibonacci sequence, a series of numbers wherein each number is added to the last. The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on, with the ratio of each number and the previous number gradually approaching 1.618, or phi.

History of the golden ratio.

The first known mention of the golden ratio is from around 300 BCE in Euclid’s  Elements , the Classical Greek work on mathematics and geometry. Euclid and other early mathematicians like Pythagoras recognized the proportion, but they didn’t call it the golden ratio. It wasn’t until much later that the proportion would take on its mystique. In 1509, Italian mathematician Luca Pacioli published the book  De divina proportione , which, alongside illustrations by Leonardo da Vinci, praised the ratio as representing divinely inspired simplicity and orderliness.

Because of Pacioli’s book and Leonardo’s illustrations, the golden ratio gained fame among mathematicians and artists. In the centuries since Pacioli’s book, many enthusiasts have claimed that the number is naturally pleasing to the eye, that it is a mathematical distillation of beauty, and that golden ratio line segments, golden rectangle side lengths, and golden triangles are represented throughout art history.

Golden ratio enthusiasts argue that the golden ratio is aesthetically pleasing because it’s common in the natural world. The proportions of nautilus shells and human bodies are examples of the golden ratio in nature, but these tend to vary greatly from one individual to the next. Some seashells expand in proportion to the golden ratio, in a pattern known as a golden spiral, but not all shells do. It’s true that nautiluses maintain the same shell proportions throughout their life, but the ratio of their shells is usually a logarithmic spiral, as opposed to an expression of phi.

Phi does show up in other aspects of nature. Tree leaves and pine cone seeds tend to grow in patterns that approximate the golden ratio, and sunflower spirals and other seeds tend to hew close to phi. Phi allows for efficient distribution or packing, so leaves that grow in relation to the golden ratio will not shade each other and will rest in relation to one another at what is known as the golden angle.

There’s no evidence that use of the golden ratio is better than use of other proportions, but artists and designers are always in the business of creating balance, order, and interesting composition for their work.

The golden ratio in art and graphic design.

A few artists and designers have deliberately based their work around the golden ratio. Le Corbusier, a famous mid-century modern architect, based a good deal of his architectural system around the golden ratio. Salvador Dali, the surrealist painter, intentionally used a canvas shaped like a golden rectangle for his painting  The Sacrament of the Last Supper . In 2001, American prog-metal band Tool released “Lateralus,” a song with Fibonacci-inspired time signatures.

Art historians have found other examples of the golden ratio in the  Mona Lisa , the Parthenon in ancient Athens, and the Great Pyramid of Giza. However, most of the time there is no explicit evidence that artists intentionally used the ratio the way Le Corbusier, Dali, or Tool did. Without design notes or specifications for the pyramids, we can’t know if ancient engineers employed phi on purpose.

How to use the golden ratio in your work.

Aesthetics and design don’t adhere to strict mathematical laws. You can create a poor design that still conforms to the golden ratio, but you can use the golden ratio to inform your composition, to help you avoid clutter and create an orderly and balanced design. “On a graphic that might be pretty busy, so placement is everything,” says graphic designer Jacob Obermiller. You can use the golden ratio to help guide you.

The golden ratio can work a bit like the  rule of thirds : It can be a compositional convention or guide, but not a hard-and-fast regulation about how you should structure your work. Ultimately, spacing is important and any kind of guideline is helpful. “If everything is important, then nothing is important,” says human factors engineering student Sara Berndt. If you just center every image or arrange text as a single unjustified block, you risk alienating your reader, viewer, or user. Use the golden ratio as a guideline for your work to make sure things are nicely spaced out and well composed.

With a convention like the rule of thirds or golden ratio, you can create variation and blank space that pleases the eye and makes content easy to comprehend. “The golden ratio is all about blank space and its relation to the ‘pay attention’ space,” says Berndt. “There’s only so much that people can take visually. This is a guiding principle to help you understand the limits of human attention so you can create something that is aesthetically pleasing.”

If you decide to use the golden ratio as a basis for your art or design, it can help your project look even, balanced, and aesthetically pleasing. But your ratios don’t have to be exactly 1.618 as long as you design deliberately and creatively. Regardless of the ratios and proportions you use,  Adobe Illustrator  can help you craft your work so everything is balanced to your own golden specifications.

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Jacob Obermiller ,  Sara Berndt

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Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks

Today I will be discussing what the  golden ratio is (otherwise known as the golden mean) and how we can use it to improve your artwork .

What Is the Golden Ratio?

Calculations, the golden rectangle, the fibonacci sequence, golden spiral, applying the golden ratio in art, examples of the golden ratio, want to learn more, thanks for reading.

I’ll walk you through the entire process using one of my recent paintings. You’ll see how I go from idea all the way through to reflecting on the finished painting.

The golden ratio is the ratio of approximately 1 to 1.618 . These are extremely important numbers to mathematicians. But what do they mean to us artists?

Well there have been studies which suggest designs set out using the golden ratio are aesthetically pleasing. We can use the golden ratio to help design our paintings and position our subjects.

Who would have thought art and maths could have such a close connection? Luca Pacioli (a contemporary of Leonardo da Vinci) went as far as saying:

“Without mathematics there is no art.” 

The golden ratio has been around for some time and has influenced many areas of life, including architecture, maths, design and of course art.

Here is a rough timeline of the golden ratio’s history according to author Priya Hemenway:

• Phidias  (490-430 BC) made the  Parthenon  statues that seem to embody the golden ratio.
• Euclid  (c. 325-c. 265 BC), in his  Elements , gave the first recorded definition of the golden ratio, which he called, as translated into English “extreme and mean ratio”.
• Fibonacci  (1170-1250) mentioned the numerical series now named after him in his  Liber Abaci. We will discuss the Fibonacci sequence later in this post.
• Luca Pacioli  (1445-1517) defines the golden ratio as the “divine proportion” in his  Divina Proportione .
• Charles Bonnet  (1720-1793) points out that in the spiral phyllotaxis of plants going clockwise and counter-clockwise were frequently two successive Fibonacci series.
• Martin Ohm  (1792-1872) is believed to be the first to use the term  goldener Schnitt  (golden section) to describe this ratio, in 1835.
• Édouard Lucas  (1842-1891) gives the numerical sequence now known as the Fibonacci sequence its present name.

I will try and keep this simple (as we do not need to understand all the complexities of the golden ratio as artists). 

The golden ratio can be calculated as follows:

That weird symbol at the end represents the golden ratio.

I find this equation easier to understand in pictural format:

So a+b is to a as  a  is to  b .

Confused yet? Keep reading as it becomes easier to understand when we apply it to certain situations.

Below is a  golden rectangle , which means the side lengths are in golden ratio. If you take away that square on the left, another rectangle will remain which is also in golden ratio. This could continue indefinately.

There is some kind of peacefulness and beauty in infinite numbers, which is possibily why the golden ratio is so popular in design.

Creating the golden rectangle is easy using these steps. All you need is a compass.

Step 1 – Construct a simple square.

Step 2 – Draw a line down the middle of the square.

Step 3 – Grab your compass and place one point at the intersection at the bottom middle and draw down from the edge of top right corner, as shown below.

Step 4 – Complete the golden rectangle.

Note: This is for demonstration purposes only so it may not be the exact proportions of the golden ratio. 

The following is the Fibonacci sequence : 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, … The next number is found by adding up the two numbers before it.

When we take any two successive (one after the other) in the sequence,  their ratio is very close to the golden ratio .

In fact, the later the numbers are in the sequence, the closer it becomes to the golden ratio.

This relationship between the Fibonacci sequence and the golden ratio is shown below:

The golden spiral is what occurs when you spiral a line through the golden rectangle.

This  spiral can be found throughout nature:

Now we can get to some of the more interesting applications of the golden ratio.

The golden ratio has been used by artists to locate aesthetically pleasing areas to place our subjects and distribute weight in our paintings.

The Eyes Of The Golden Rectangle

One technique is to use the “eyes of the rectangle” to position your subjects. These “eyes” are indicated in blue below:

The Golden Section

Another option is to segment your painting into nine unequal sections using the golden ratio.

The ratio of the columns is 1: 0.618: 1. Likewise for the rows.

You can then use this diagram as a tool to ensure there is balance throughout your composition. I will show you some examples below.

This is a more complex version of the rule of thirds . The application of the golden section and the rule of thirds is basically the same.

I could use the golden ratio to design this very website in an aesthetically pleasing manner. For example, I could distribute the content to sidebar widths according to the golden ratio.

I could also use the golden ratio to determine the size of my header in relation to my content, or my logo to my menu. There is no limit to how I could use the golden ratio.

This is not to say my website is designed strictly using the golden ratio – this is just for demonstration purposes.

The Golden Ratio In Paintings

In this painting by Georges Seurat, the golden ratio appears to have been used throughout the painting – to define the horizon, to place points of interest and to create balance in what would appear to be a very active scene.

Georges Seurat also seems to have used the  golden ratio in this painting. Notice the positioning of the jetty, the sail mast and the horizon.

This contemporary peice needs little explanation. It is just an arrangement of golden rectangles and colors.

Take note of the position of the table and the edge of the ceiling in this painting by Salvador Dali, who seems to have used the golden ratio to help design a number of his paintings.

The golden ratio even appears to have been used in this classic painting by Michelangelo.

I hope this post helps you understand the importance of the golden ratio in art and design. But, as with many other art concepts, the golden ratio is just a tool to assist you. Do not end up being confined by always needing to follow the golden ratio.

The majority of famous paintings do not follow the golden ratio. But by using the golden ratio you may have a greater chance of your painting being aesthetically appealing.

If you want to learn more, refer to my detailed guide on composition .

You might be interested in my  Painting Academy  course. I’ll walk you through the time-tested fundamentals of painting. It’s perfect for absolute beginner to intermediate painters.

I appreciate you taking the time to read this post and I hope you found it helpful. Feel free to share it with friends.

Happy painting!

Draw Paint Academy

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Dan Scott is the founder of Draw Paint Academy. He's a self-taught artist from Australia with a particular interest in landscape painting. Draw Paint Academy is run by Dan and his wife, Chontele, with the aim of helping you get the most out of the art life. You can read more on the About page .

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22 comments on “Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks”

i read about the golden ratio before and have no idea how to use it and where to apply it. i spend good time reading your explanation and where to use it make a lot of sense to me. thank you very good and easy to understand and we have the option to use it or not. thanks again

Thanks for the informative post!

Dan Great post. I’ve read much about the Golden Ratio and it’s an absolute classic. I’m a beginner and I’d rather follow proven techniques than muddle through by myself. Many Thanks.

Hi Dan, I enjoyed this article, very informative as usual. But golden ratio ?? Colour me dumb. I just paint by the seat of my pants ( instinct). I will continue following your articles, there is always something to learn, even for a fossil like yours truly. Keep ’em coming Dan.

Thanks David! More to come. Dan

Thank you David! Your presentation of Golden Ratio as a scientific tool for artists was very exciting for me! I have been familiar with the golden ratio and its calculation, but its application by painters was absolutely new! I learned a lot!

I learned something new today. I knew about the rule of thirds but not about the golden ratio. Thank you. I am a photographer and have used my gut to tell me what looks right. I am sure that I have a lot to learn.

I understand the rule, but am having a hard time visualizing it in a painting that I want to set up.

As so many others, I am a beginner. I knew about the Golden Ratio and what it was so I thought it would be a doddle when it was recently touched upon in an art class. Unfortunately, I very much struggled to train my eye to see both it and the Rule of Thirds or rather to apply it to my efforts. I am so glad my search brought me to this page. This is the first time someone has explained it in an approachable, practical and clear way.

Many, many thanks

it’s aesthetically not aethetically.

For years, I used an old Disney short film, “Donald in Mathemagic Land” teaching my undergrad intro to Philosophy classes. The imagery is too dated now for students (e.g. rotary dial phones) but the range and variety of examples of the Golden Section is still captivating. It was always a great preview to hitting them with logic. Thank you for your post. It is a great explanation of a complex topic.

Just watched it again today! Yes!

Way cool! I just googled golden rectangle because I wanted to make a clay box. Read down about the golden spiral which I had seen previously but didn’t know the mathematics behind it. Great information with clear explanation. Thank you!

Seurat also seems to utilize a spiral within the composition of his figures in the Bathers painting but I don’t know whether it has the Golden ratio.

thanks, I finally understand the golden ratio.

Thank you. What a clear explanation of the Golden Mean. Not so scared of it now.

A great read & one of the more well explained articles I’ve read on the rule.

One of the things I always wonder though is: were these great works planned out as golden ratio pieces or did the artists just put together something aesthetically pleasing and it happens to ‘fit’ the formula.

For example, ive had students and collectors note that some of my work fits the golden ratio – to which i will nod and smile – even though I myself have never actually set out to design it this way. lol

The Mondrian painting are not just squares, sort of speak. Mondrian used a much deeper explanation for the use of color, each color has a separate meaning, for example. He was very serious in that. Maybe interesting for those who did not know this fact.

Thankyou this is such a fantastic explanation!

Thank you very much for this explanation, Dan. Very thorough but easy to understand.

Thanks so much! I now apply the information to my prints and paintings to see if I can accentuate or shift for balance and goldenness.

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Golden Ratio in Art – Learn How to Use the Golden Ratio in Art

The golden ratio, also known as “Phi” and more popularly known as the Fibonacci Sequence, is an irregular equation. A ratio of 1 to 1.618 is what is referred to as an irrational number, similar to that of the famous Einstein equation “pi”. For the sake of beautiful aesthetics, this ratio can be a helpful tool for capturing balance and pleasing proportional values within your artwork. The idea is that it is a perfect rectangle, and when divided into uneven halves with a perfect square on one side, the leftover rectangle will have the same proportions as the original perfect rectangle. If this shape is continuously divided into two using the ratio, it will always result in a perfect or golden rectangle and square. Once you know how to draw this particular geometric sequence, it can be a great tool to harmonize and balance out your own artwork’s compositional value.

Table of Contents

• 1.1 Necessary Materials
• 1.2 Preparation
• 2.1 What Is the Golden Ratio in Art?
• 2.2.1 Understanding the Sequence in Numbers
• 2.2.2 Understanding the Sequence in Geometry
• 2.2.3 Drawing the Golden Spiral
• 2.2.4 Going Over the Spiral with Ballpoint Pen
• 2.2.5 Highlighting the Squares and Rectangles
• 3.1 Golden Ratio in Landscapes
• 3.2 Golden Ratio in Portraiture
• 3.3 Seeking Out the Golden Ratio in Nature
• 4 Tips to Remember
• 5.1 Does the Golden Ratio Create Perfect Balance within Artwork?
• 5.2 Can You Apply the Golden Ratio to Various Subject Matter?

An Easy Guide to Using the Golden Ratio in Art

In this tutorial, we will be introduced to the golden ratio, seeing how this particular equation has influenced some artworks and how we can use this sequence in our work. Beneath the complicated versions of both understanding and using this ratio, we will find in this tutorial that it is quite a simple algorithm and quite helpful for aesthetic composition within an artwork.

There are also various ways to create a Fibonacci sequence and, in this tutorial, we will be looking at the most helpful way to use this sequence in its most basic format.

Necessary Materials

Learning how to use the golden ratio starts with understanding the basics. We don’t need many materials for this foundational approach to learning the Fibonacci ratio. What we will need is a ruler, a pencil, a ballpoint pen, and a compass. We will also want to make sure that we have an eraser on hand as well as a sharpener for any silly mistakes and to keep our pencils sharp for fine lines. All the materials can be found through the different links below:

• Ballpoint pen
• Good paper (200 g/m – 250 g/m recommended)

Preparation

Once we have all our necessary materials, we will want to place ourselves within an environment whereby it will help us to focus on the tutorial at hand. The golden ratio can be a little tricky to understand so you will want to have your full engagement within this tutorial, at least for the first half.

Once we have the process figured out, we then can play around with how we use it in our work to set up an aesthetically balanced composition.

How to Use the Golden Ratio in Art

In this tutorial, we will look at some examples of how the golden ratio has been used within the genre of art. We want to build up an understanding of the unique sequence and how it has been used to apply it as best we can to our work. We will then move on to learning how to draw the golden ratio using the correct sequence.

From there we will create a landscape drawing that describes how to apply it to your artwork. Now that we know what we should expect from this tutorial on how to draw the golden ratio, let’s get started!

What Is the Golden Ratio in Art?

The existence of the golden ratio is an eternal universal force in one sense as it could be said that all mathematical formulas and equations are embedded into the known universe. In humanity’s history, it was popularized by Euclid himself (who is responsible for Euclidian geometry) around 365 BC.

However, the term “Golden Ratio” was coined by Martin Ohm in the 1800s and from there was then designated the name “Phi” in the 1900s by an American mathematician Mark Barr.

The book was illustrated by Leonardo Da Vinci, whereby it is speculated that the sequence of the golden ratio was used to create various drawings, including the famous “ Vitruvian Man “.

This means that the Fibonacci sequence or golden ratio will be easy to find in artworks with natural elements as they will inevitably be formed by the laws of the universe.

How to Draw the Golden Ratio

Just because the Fibonacci sequence is a commonly occurring pattern doesn’t mean it’s a useless tool, in fact learning how to use the golden ratio in paintings and drawings is essential for an artist. It provides the artist with a deeper understanding of configuring an artwork to have well-balanced proportions and composition.

There are many ways to learn this skill that is challenging and confusing but we will learn the basic and most helpful way to draw the golden ratio.

Understanding the Sequence in Numbers

Firstly, we want to break down the basic formula of the Fibonacci sequence, which is understood in an equation but is most easily understood as a number sequence. It goes as follows: if you start at 0 and add 1, you will have 1 as a result. By nature of the sequence, you have two 1’s, which equals 2. From there, your next two numbers to add will be 1 and 2, which give you three, then 3 and 2, which give you 5, and so on.

The number formula is as follows: every previous number added to the current number will equal the next number. This sequence is infinite.

Understanding the Sequence in Geometry

How this plays out in a geometric formula is quite simple as well and easily transferable, the magic of math. For instance, if we start with a single line and keep to the same measurement size for a single block, we can eventually build up the golden ratio.

Starting with your ruler draw a single horizontal line.

Start with a single square, evenly sized on your horizontal line.

You will find that every time you turn your page clockwise from this point on, the previous blocks have set up the number of blocks needed for the next square.

If you don’t want to turn your page you can also imagine drawing each next perfect square in an anti-clockwise format.

Again, if you stick to the same scale of blocks and work in an anti-clockwise direction, the previous blocks will have been set up both in number and block the number of blocks needed for the next square.

Essentially, we are drawing a set of perfect squares in a circle that get larger and larger, determined by the number sequence.

If you have kept your page on the table, unmoved, you should have worked around each square in an anti-clockwise movement each time.

You can also write out the number sequence to give yourself a double-check to see if your arrangement of squares correlates with the sequence of numbers.

Drawing the Golden Spiral

Using your compass and pencil we now going to draw in a clockwise motion a curve within each square. Starting with the largest square, we want to draw a curvature that will run from the corners of each square flowing into the next smaller one.

Technically, we are working backward now from largest square to smallest square.

Then you readjust your compass for the next curve and so on.

You can freehand it but make sure you take your time and go about it slowly, but at that point, it doesn’t matter.

Going Over the Spiral with Ballpoint Pen

To emphasize the spiral within the shapes, connect it to your compass and go over the curved lines drawn in pencil. We just want to emphasize the flow of the spiral and how its curvature changes subtly as it enters the next smaller square.

This is the amazing part of math, if your measurements are correct, you can determine the results correctly.

Highlighting the Squares and Rectangles

This next part is more for fun to show you how the golden ratio makes the squares and rectangles inseparable. This is because the geometry of the sequence establishes an intertwining of the two shapes.

If you go over the squares with one color and the rectangles with another, you will always overlap in color every time.

Tips on How to Use the Golden Ratio in Art

There are a few ways one might be able to use the golden ratio in their work. There are various ways to use the golden ratio but perhaps the most powerful way to use it is as an invisible guiding force. By this, what is meant is that the golden ratio has a blueprint utility, whereby it is used as a diagram.

Golden Ratio in Landscapes

For instance, the golden ratio should not be considered a mandatory formula for perfect aesthetics. However, it can be a great tool for guiding a scene. For instance, once you know how to draw the golden ratio, you can then use the mathematical proportions to set up the flow of a scene.

By creating a golden ratio composition, you will find that the work has more harmonization amongst its elements.

Golden Ratio in Portraiture

There are many instances where the golden ratio has been used to assist the process of drawing or painting portraits. Again, this doesn’t mean that it is a hard and fast rule for aesthetics but its mathematical rules can be applied to creating symmetry within faces. When it comes to the human face, symmetry is a key element of the face due to the formation of the skull, and capturing that can be difficult.

The adjustability of the golden spiral and rectangle can also be used as a measuring tool to establish features on the face.

The Golden spiral can be a great assistance for capturing symmetry even when there is a distortion in scale due to perspective.

Seeking Out the Golden Ratio in Nature

The point is the golden ratio can be found quite often because it works according to the laws of physics as does nature. This means its bending and spiral-like quality often is found in all sorts of natural elements and creatures because all nature is subjected to physical laws. The point is to seek it, now that you know how the formula works and how to apply it, allow yourself to use it in all sorts of ways.

Give yourself the creative freedom to explore the potential of the golden ratio within your artwork.

Tips to Remember

• Get comfortable with the Golden Ratio. Learn how it works and have it locked in your brain before exploring how to use the golden ratio in art.
• Explore its potential. As you learn how to use the golden ratio in art, you will find that it can be applied to all sorts of genres in all sorts of ways.
• It is useful for abstract works as well. Another realm to explore is the abstract art genre, where geometric harmony can be explored in its full potential.
• Manipulate it. The golden ratio is something that can be changed in size, direction, inverted, and so on. Play around with duplicating it, changing its scale, and exploring how else it can be used.
• Do more research. Do some research into the golden ratio and see how artists you might find inspiring have used it in their work.
• Have fun with it! Using the golden ratio in paintings and drawings is a great way to explore the functionality of the golden ratio.

Learning about what is the golden ratio in art is an open-ended conversation because there are no mandatory ways in which the golden ratio should be used. It’s a strange phenomenon that has a lot of potential for exploration and its utility is quite broad. Learning the golden ratio in art reveals more each time you use it. Understanding golden ratio composition becomes applicable to more and more genres of art, it is all just a matter of curiosity and exploration.

Frequently Asked Questions

Does the golden ratio create perfect balance within artwork.

The golden ratio’s geometric sequence will constantly create an infinite supply of perfect rectangles and squares, also known as golden rectangles and squares. This geometric formation enables a seemingly perfect harmonization aesthetically when it comes to the composition of elements within space. That being said, the golden ratio composition is more speculation as it does not always guarantee that the use of its ratio results in a perfect balance of aesthetics. The idea is that it is a tool for symmetry or balance, however, it is a complicated geometric structure that can be deviated from or tweaked when applied to your own artwork. The golden ratio in paintings and drawings is often found more than placed as it is an easy structural formation that forms more than it is an intentional choice. However, if used intentionally it can be a great way to create unique aesthetic proportional values within an artwork.

Can You Apply the Golden Ratio to Various Subject Matter?

By nature of the divisional process of the golden ratio, it becomes a naturally occurring structure that is often found in various spaces, photographs, and artworks. This means that because of its infinite division, it is an adaptable structure that can be applied to multiple forms. In the case of art, it can be an excellent tool for portraiture, architectural design, landscape, and various artwork ideas. Although its geometric nature is unique and recurring it doesn’t mean it’s a perfect rule that should always be used. Knowing the golden ratio in art and then using the golden ratio in art is more a matter of subjective choice for formulating a composition. It is a very beautiful geometric sequence that does help to create qualities of symmetry and balance and works for all subject matter. That being said, it is only a tool that should be used if it is necessary for a specific desired outcome, apart from that it should not be considered a golden rule.

Matthew Matthysen is an educated multidisciplinary artist and illustrator. He successfully completed his art degree at the University of Witwatersrand in South Africa, majoring in art history and contemporary drawing. The focus of his thesis was to explore the philosophical implications of the macro and micro-universe on the human experience. Matthew uses diverse media, such as written and hands-on components, to explore various approaches that are on the border between philosophy and science.

Matthew organized various exhibitions before and during his years as a student and is still passionate about doing so today. He currently works as a freelance artist and writer in various fields. He also has a permanent position at a renowned online gallery (ArtGazette) where he produces various works on commission. As a freelance artist, he creates several series and successfully sells them to galleries and collectors. He loves to use his work and skills in various fields of interest.

Matthew has been creating drawing and painting tutorials since the relaunch in 2020. Through his involvement with artincontext.org, he has been able to deepen his knowledge of various painting mediums. For example, watercolor techniques, calligraphy and lately digital drawing, which is becoming more and more popular.

Learn more about Matthew Matthysen and the Art in Context Team .

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The Most Famous Artists and Artworks

Discover the most famous artists, paintings, sculptors…in all of history! 

MOST FAMOUS ARTISTS AND ARTWORKS

Discover the most famous artists, paintings, sculptors!

Golden Ratio

The golden ratio (symbol is the Greek letter "phi" shown at left) is a special number approximately equal to 1.618

It appears many times in geometry, art, architecture and other areas.

The Idea Behind It

Have a try yourself (use the slider):

This rectangle has been made using the Golden Ratio, Looks like a typical frame for a painting, doesn't it?

Some artists and architects believe the Golden Ratio makes the most pleasing and beautiful shape.

Do you think it is the "most pleasing rectangle"?

Maybe you do or don't, that is up to you!

Many buildings and artworks have the Golden Ratio in them, such as the Parthenon in Greece, but it is not really known if it was designed that way.

The Actual Value

The Golden Ratio is equal to:

1.61803398874989484820... (etc.)

The digits just keep on going, with no pattern. In fact the Golden Ratio is known to be an Irrational Number , and I will tell you more about it later.

We saw above that the Golden Ratio has this property:

a b = a + b a

We can split the right-hand fraction then do substitutions like this:

a b = a a + b a ↓      ↓      ↓ φ =  1 + 1 φ

So the Golden Ratio can be defined in terms of itself!

Let us test it using just a few digits of accuracy:

With more digits we would be more accurate.

Powers (Exponents)

Let's try multiplying by φ :

φ = 1 + 1 φ ↓     ↓     ↓ φ 2 = φ + 1

That ended up nice and simple. Let's multiply again!

φ 2 = φ + 1 ↓     ↓     ↓ φ 3 = φ 2 + φ

The pattern continues! Here is a short list:

Note how each power is the two powers before it added together! The same idea behind the Fibonacci Sequence (see below).

Calculating It

You can use that formula to try and calculate φ yourself.

First guess its value, then do this calculation again and again:

• A) divide 1 by your value (=1/value)
• C) now use that value and start again at A

With a calculator, just keep pressing "1/x", "+", "1", "=", around and around.

I started with 2 and got this:

It gets closer and closer to φ the more we go.

But there are better ways to calculate it to thousands of decimal places quite quickly.

Here is one way to draw a rectangle with the Golden Ratio:

• Draw a square of size "1"
• Place a dot half way along one side
• Draw a line from that point to an opposite corner
• Now turn that line so that it runs along the square's side
• Then you can extend the square to be a rectangle with the Golden Ratio!

(Where did √5 2 come from? See footnote*)

A Quick Way to Calculate

That rectangle above shows us a simple formula for the Golden Ratio.

When the short side is 1 , the long side is 1 2 + √5 2 , so:

φ = 1 2 + √5 2

The square root of 5 is approximately 2.236068, so the Golden Ratio is approximately 0.5 + 2.236068/2 = 1.618034. This is an easy way to calculate it when you need it.

Interesting fact : the Golden Ratio is also equal to 2 × sin(54°) , get your calculator and check!

Fibonacci Sequence

There is a special relationship between the Golden Ratio and the Fibonacci Sequence :

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

(The next number is found by adding up the two numbers before it.)

And here is a surprise: when we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio .

In fact, the bigger the pair of Fibonacci Numbers, the closer the approximation.

Let us try a few:

We don't have to start with 2 and 3 , here I randomly chose 192 and 16 (and got the sequence 192, 16,208,224,432,656, 1088, 1744, 2832, 4576, 7408, 11984, 19392, 31376, ... ):

The Most Irrational

I believe the Golden Ratio is the most irrational number . Here is why ...

So, it neatly slips in between simple fractions.

Note: many other irrational numbers are close to rational numbers, such as Pi = 3.14159265... is pretty close to 22/7 = 3.1428571...)

No, not witchcraft! The pentagram is more famous as a magical or holy symbol. And it has the Golden Ratio in it:

• a/b = 1.618...
• b/c = 1.618...
• c/d = 1.618...

Read more at Pentagram .

Other Names

The Golden Ratio is also sometimes called the golden section , golden mean , golden number , divine proportion , divine section and golden proportion .

Footnotes for the Keen

* where did √5/2 come from.

With the help of Pythagoras :

c 2 = a 2 + b 2

c 2 = ( 1 2 ) 2 + 1 2

c 2 = 1 4 + 1

c = √( 5 4 )

Solving using the Quadratic Formula

We can find the value of φ this way:

Which is a Quadratic Equation and we can use the Quadratic Formula:

φ = −b ± √(b 2 − 4ac) 2a

Using a=1 , b=−1 and c=−1 we get:

φ = 1 ± √(1+ 4) 2

And the positive solution simplifies to:

Kepler Triangle

That inspired a man called Johannes Kepler to create this triangle:

It is really cool because:

• it has Pythagoras and φ together
• the ratio of the sides is 1 : √φ : φ , making a Geometric Sequence .

InVisionApp, Inc.

Inside Design

A guide to the Golden Ratio for designers

Emily esposito,   •   oct 19, 2018.

G ood design has been up for debate for as long as we’ve been creating. There are endless forums, social media threads, and in-person conversations about what makes for great design, with everyone contributing their own point of view.

That’s the beauty of design, right? Everyone can interpret it differently.

Top Stories

While there will never be a one-size-fits-all approach for design, there is a concrete, mathematical approach that can help us get one step closer to creating amazing design experiences every time: the Golden Ratio.

The Golden Ratio is a mathematical ratio you can find almost anywhere, like nature, architecture, painting, and music. When specifically applied to design specifically, it creates an organic, balanced, and aesthetically pleasing composition.

In this article, we’ll dive into what the Golden Ratio is, how to calculate it, and how to use it in design—including a handy list of tools.

What is the Golden Ratio?

Also known as the Golden Section, Golden Mean, Divine Proportion, or the Greek letter Phi, the Golden Ratio is a special number that approximately equals 1.618. The ratio itself comes from the Fibonacci sequence, a naturally occurring sequence of numbers that can be found everywhere, from the number of leaves on a tree to the shape of a seashell.

The Fibonacci sequence is the sum of the two numbers before it. It goes: 0, 1,1, 2, 3, 5, 8, 13, 21, and so on, to infinity. From this pattern, the Greeks developed the Golden Ratio to better express the difference between any two numbers in the sequence.

How does this relate to design? You can find the Golden Ratio when you divide a line into two parts and the longer part (a) divided by the smaller part (b) is equal to the sum of (a) + (b) divided by (a), which both equal 1.618. This formula can help you when creating shapes, logos, layouts, and more.

You can also take this idea and create a golden rectangle. Take a square and multiple one side by 1.618 to get a new shape: a rectangle with harmonious proportions.

If you lay the square over the rectangle, the relationship between the two shapes will give you the Golden Ratio.

“While there will never be a one-size-fits-all approach for designing, there is a concrete, mathematical approach that can help us get one step closer to creating amazing design experiences every time: the Golden Ratio.”

If you keep applying the Golden Ratio formula to the new rectangle on the far right, you will end up with an image made up of increasingly smaller squares.

If you draw a spiral over each square, starting in one corner and ending in the opposite one, you’ll create the first curve of the Fibonacci sequence (also known as the Golden Spiral).

101 quotes about design, collaboration, & creativity

How to use the golden ratio in design.

Now that the math lesson is over, how can you apply this knowledge to the work you do on a daily basis?

Here are four ways to use the Golden Ratio in design:

1. Typography and defining hierarchy

The Golden Ratio can help you figure out what size font you should use for headers and body copy on a website, landing page, blog post, or even print campaign.

Let’s say your body copy is 12px. If you multiply 12 by 1.618, you’ll get 19.416, meaning a header text size of 19px or 20px would follow the Golden Ratio and balance the 12px body font size.

If you want to figure out how big your body text size should be, you could do the opposite. If your header text is 25px, you can divide it by 1.618 to find the body text (15 or 16 px).

2. Cropping and resizing images

When cropping images, it’s easy to identify white space to cut out. But, how do you make sure the image is still balanced after you resize it? You can use the Golden Spiral as a guide for the image’s composition.

For example, if you overlay the Golden Spiral on an image, you can make sure that the focal point is in the middle of the spiral.

Leveraging the Golden Ratio can help you design a visually appealing UI that draws the user’s attention to what matters the most. For example, a page that highlights a wide block of content on the left with a narrower column on the right can follow the Golden Ratio’s proportions and help you decide where to put the most important content.

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4. logo development.

If you’re designing a new logo and feeling stuck, turn to the Golden Ratio to help you sketch out the proportions and shapes. Many popular logos follow the Golden Ratio, like Twitter, Apple, and Pepsi.

Photo credit: Mostafa Amin and Brandology Studio

Designer Kazi Mohammed Erfan even challenged himself to create 25 new logos entirely based on the Golden Ratio. The result? Simple, balanced, and beautiful icons.

Photo credit: Kazi Mohammed Erfan

Tools to help you use the golden ratio.

You don’t need to break out the pencil and paper to calculate the Golden Ratio — there are a number of apps that can do it for you.

Here are five tools to help you use the Golden Ratio in your designs:

• Golden Ratio Calculator: Calculate the shorter side, longer side, and combined length of the two sides to figure out the Golden Ratio.
• goldenRATIO : Created for designers and developers, this app gives you an easy way to design websites, interfaces, layouts, and more according to the Golden Ratio. It includes a built-in calculator with visual feedback and features to store screen position and settings, so you don’t have to rearrange the Golden Ratio for every task.
• Golden Ratio Typography Calculator : Discover the perfect typography for your website by entering your font size and width. You can optimize based on font size, line height, width, and characters per line.
• PhiMatrix : This Golden Ratio design and analysis software comes customizable grids and templates that you can overlay on any image. It can be used for design and composition, product design, logo development, and more.
• Golden Ratio Sketch resource : Download a free Sketch file of the Golden Spiral to help with image and layout composition.

Getting started with the Golden Ratio

Once you know what to look for, you’ll start noticing the Golden Ratio everywhere. (Don’t believe us? Look at your hands. Even your fingers follow the Golden Ratio.) The human eye is used to seeing this magical number and we subconsciously react positively to it.

As designers, we can use this number to our advantage. Even small tweaks to the way you crop an image or develop a layout can dramatically improve how your users interact with your design.

Watch it now.

by Emily Esposito

Emily has written for some of the top tech companies, covering everything from creative copywriting to UX design. When she's not writing, she's traveling the world (next stop: Japan!), brewing kombucha, and biking through the Pacific Northwest.

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The Golden Ratio - Principles of form and layout

Now, we’re going to look at a subject that comes directly from mathematics and that we can also find all around us – the golden ratio . Don’t worry; we’re not going back into the classroom for long. We will examine what this concept is and exactly how much it is a fundamental part of making designs pleasing to the user’s eye.

The golden ratio’s story is the stuff of legend. With a history dating back almost to the time of Pi (another great mathematical formula, which is essential in understanding properties of circles), scholars, including Pythagoras and Euclid, have called it by many names, including the golden mean and the divine section .

What is the appeal of this ratio? For centuries, it has been thought that art, architecture and nature are more appealing to the eye when the proportions of designs and structures are based on the golden ratio. You can find examples of the golden ratio in human endeavors as far back as Ancient Greece. The Parthenon statues appear to show the golden ratio in their form, and some of Plato’s five solids (including the cube and the dodecahedron) are related to it, too. The golden ratio was popularized in the Renaissance era, and the artists of that period sought to ensure that it was used to deliver aesthetically pleasing works. Today, we can use the golden ratio in our web and app designs to improve the layout and appeal to the eye, placing full confidence in this time-honored fact.

What Is the Golden Ratio?

The Golden Ratio has been used throughout history to create visually appealing designs. In the Renaissance, it became a formalized part of design theory . Its frequent appearances in geometry (in such shapes as pentagons and pentagrams) drew the attention of ancient Greek mathematicians, who began studying it at least 2400 years ago. The ratio is based on the relationship between consecutive numbers in the Fibonacci sequence. Fibonacci was a medieval Italian mathematician; however, you don’t need to be a mathematician to understand this sequence, as it is so simple.

Each number in the Fibonacci sequence is simply the sum of the two numbers before it. It begins with 1, 1 (i.e., 1 + the unseen 0 = 1), and the first 10 members of the sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55. It continues infinitely. We can calculate the ratio using the formula above (we use the Greek letter Phi to represent the output). The ratio is approximately 1.618, although, like Pi , it has a long string of numbers after the decimal point. For our purposes, though, we don’t have to worry about going past 1.618.

How is the ratio used in design? Think of a rectangle, with a short side of length 1. To calculate the most aesthetically pleasing rectangle, you simply multiply the length of the short side by the golden ratio approximation of 1.618. So, the long side, in this instance, would have a length of 1.618.

If you have a pencil, paper and ruler handy, try drawing a rectangle of this scale. Or, if you can jump to another screen, create one in a drawing application. What you will see before you is not just any rectangle but the ideal rectangle!

We can find the golden ratio throughout the world of design. The architects of the day used it for the base and height of the Acropolis in Greece. It’s used to determine the format of the vast majority of books on your physical bookcase. It’s literally everywhere you look. Perhaps because we’re surrounded by figures and shapes derived from the golden ratio, we’ve grown especially used to it. As designers, we need to keep this concept of comfort and familiarity in mind for our users. The eyes of the world view this ratio favorably. Literally, in fact: the magazine National Geographic uses a yellow rectangle proportioned according to the golden ratio.

However, the golden ratio doesn’t help us just to make nice rectangles. You can also form a spiral using side lengths based on the decreasing order of the Fibonacci sequence. So, if we take a length 55 as our starting point, we can make our spiral by drawing it inwards so that when it passes that starting point, the new length is 34. We continue working inwards with lengths of 21, 13, 8, 5, etc. until we get to the middle (length = 1). This spiral is also based on the golden ratio and can be more interesting than an equally balanced spiral to the human eye. It is present in nature, ranging from plants to shellfish and mollusks. Even the specific proportions of many larger animals (including humans!) are often said to be proportioned according to the golden ratio. In that sense, it could be said that it’s a part of us. So, you as a designer can use this kind of spiral to catch the eyes of users from any part of the world and focus them on a particular point in your design. Research has shown that the human eye identifies (and the brain interprets and processes) images based on the golden ratio more quickly than it does images that do not incorporate the ratio.

We can also use the golden ratio to balance elements within other elements. The logos of Toyota and Pepsi make use of this fact. Toyota uses the ratio to balance the ovals within their logo, and Pepsi uses it to balance the circles in theirs. Can you think of any other brands that exploit this “magic” ratio? Perhaps it’s what can make logos truly iconic!

Calculating the Golden Ratio

Let’s briefly get down to some mathematics now. As with the image shown at the top of this lesson, the equation for calculating the ratio is simple. It is the relationship between two sides of a design (usually the horizontal and the vertical). It does not matter which side we choose as the longest (A) and which we choose as the shortest (B). (Although if you are trying to see whether the golden ratio has been used in another piece, you will need to follow which side is longest or shortest.)

The formula for this is:

A/B = (A+B)/A = 1.618033987 = Φ

Φ is the Greek letter Phi – how we represent the golden ratio. Why does A/B = (A+B)/A? It does because we are following the Fibonacci sequence and A and B (if expressed in whole numbers) are simply two consecutive numbers in that sequence. Fortunately, we can approximate this to 1.6 or 1.61 or 1.618 in designs without surrendering the aesthetic appeal of the golden ratio. Our eyes aren’t bothered with such slight deviations.

How to Use the Golden Ratio in Your Designs

You can use the golden ratio in your designs easily. Taking applications such as Adobe Photoshop and Adobe Illustrator , you can create guides or layers that will help you to design using the golden ratio.

If your software doesn’t calculate the golden ratio automatically, you can always use an online tool to help specify the ratio for side lengths. Here are three such tools:

GoldenRATIO

Phicalculator

Atrise Golden Section

The Take Away

The golden ratio, which philosophers, mathematicians, architects, artists, and designers have employed for over two thousand years, is fundamental to both designers and users. Designs such as the Pepsi logo and even natural formations carrying the proportions of the golden rule, such as a nautilus shell, surround us.

Because these forms are so prevalent, our eyes identify them quickly, and we tend to process these as familiar and pleasing. Although the golden ratio has been a subject of study for centuries and was known to the ancient Greeks, the medieval Italian mathematician Fibonacci determined his famous sequence. Using this (where a series of numbers, beginning with 1,1, is such that we add the preceding number to the one following it) is the key to understanding the golden ratio (which we represent with the Greek letter Phi ).

We use the golden ratio widely in web and app design. In particular, it’s very easy to incorporate when building wireframes . You can ensure that the content you need is prioritized properly and that the aesthetic demands of the layout will be met without doing too much design work at first. Only when you, for instance, decide where you will place elements and features over this framework will the work become more involved.

In the top picture in the example above, the ratio between the content area and sidebar is equal to Phi (1.618). You can check this with the measurements below:

The total width of the fixed layout is 960 px. You divide this into a content area and a sidebar. The content area is the longer of the two areas.

If you divide the total width of 960 px by 1.618, you get 593 px. You then assign this length to the content area.

You assign the remaining 367 px to the sidebar.

As this is a ratio, it is flexible. This means that you can easily apply it to make many design layouts, as there’s no need to use fixed numbers. All you need to do is specify that the longer area is 1.618 times longer than the shorter one.

You can apply the golden ratio in any part of your page layout. For example, you could use the golden ratio within the header to grab the user’s attention and then repeat it within the body, too.

In the lower picture (above), we also see the spiral form that uses the golden ratio. Using the Fibonacci sequence in decreasing order to apply to the lengths of a spiral’s side, we can easily create spiral designs based on the golden ratio.

As designers, we find a wealth of software available that makes it easier for us to unleash the potential of the golden ratio in our creations and optimize the user experience . Adobe, with Photoshop and Illustrator, is such a company offering this great aid.

References & Where to Learn More

Hero Image: Author/Copyright holder: Matthew Oliphant. Copyright terms and licence: CC BY-ND 2.0

Friedman, V. (2008) Applying Divine Proportion to Your Web Designs . Smashing Magazine . [2014 Aug 1]

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Fibonacci and Golden Ratio

Golden spiral neon sign (Alina Kurianova, iStockphoto)

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Learn about the Fibonacci sequence and its relationship to some shapes in nature.

A Pattern in Nature

Have you ever wondered why flower petals grow the way they do? Why they often are  symmetrical  or follow a  radial  pattern. There are a lot of different patterns in nature. But one of the most well-known is the  golden ratio .

Shown is a colour photograph of a flower with white petals spread out around its yellow centre. The closest flower is in sharp focus. Many similar flowers are out of focus in the background. Each one is on a thin green stem. They are growing close together, probably in the wild.

Did you know? The golden ratio has many different names. The golden section, the golden mean, the golden proportion and the divine proportion are just a few. People have been looking for and seeing this pattern for thousands of years!

The Fibonacci Sequence  

So where does this golden ratio come from? It is based on a sequence of numbers that mathematicians around the world have been studying since about 300 BCE.

That’s around when  Acharya Pingala , an ancient Indian poet and mathematician, wrote about a pattern of short and long syllables in the lines of Sanskrit poetry. This pattern translates to a sequence of numbers called the  mātrāmeru .

The same sequence was named the  Fibonacci sequence  about 1500 years later. This is when, around 1202, Italian  mathematician Leonardo Bonacci  wrote about it in his book  Liber Abaci . Fibonacci and his writing were important to the development of mathematics in Europe. He helped introduce the Hindu-Arabic or Indo-Arabic number system to many people in the West. This system was much easier than the Roman numerals used in Italy at the time.

Did you know? Hindu-Arabic or Indo-Arabic numerals are the same number system we use today! The symbols for 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 developed in India and spread to the Middle East and North Africa. Mathematicians including al-Khwarizmi and al-Kindi first introduced the system to Europe. But it was later popularized by Fibonacci.

In  Liber Abaci , Fibonacci wrote about something called  The Rabbit Problem . It went like this:

A certain man put a pair of rabbits in a place surrounded by a wall. How many pairs of rabbits can be produced from that pair in a year, if it is supposed that every month each pair begets a new pair from which the second month on becomes productive?

( pp. 283-284, translated from original Latin)

By the end, that walled place would soon be hopping with rabbits! But how exactly would their numbers grow? Fibonacci wrote a series of numbers to solve the problem:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, …

There are zero rabbits in the first month. In the second month, one pair of rabbits move in, but they don’t have any babies for the first two months. In the fourth month, a new pair of rabbits is born! And another in the fifth. By the sixth month, both the first and second pairs are having a pair of babies every month.

These numbers are growing quickly! But did you notice the pattern? After 0 and 1, each new number is the sum of the two numbers before it. This is the Fibonacci sequence. The individual numbers within this sequence are called Fibonacci numbers.

What number comes after 4181 in the sequence above?

Did you know? “Fibonacci” was Leonardo Bonacci’s nickname. It means “son of Bonacci” in Italian. Guglielmo Bonacci was a merchant and Italian customs official. Leonardo travelled to Algeria with him, where he studied calculation. Later, Fibonacci worked and studied number systems in Egypt, Syria, Greece, Sicily, and Provence.

The Fibonacci sequence can also be expressed using this equation:

Fn = F(n-1) + F(n-2)  

Where n is greater than 1 (n>1).

The sequence gets more interesting when we divide each number by the one that comes before it.

For example: 1÷1, 2÷1, 3÷2, 5÷3, 8÷5, 13÷8, and 21÷13.

The answers would be: 1.000, 2.000, 1.500, 1.667, 1.625, and 1.615. Look at those numbers in the bar graph below. The bars are different heights, But as each set of numbers gets larger, the answer gets closer and closer to the same dotted line.

Shown is a colour bar graph with 0 - 2.0 on the y axis, and 1/1, 2/1, 3/2, 5/3, 8/5, 13/8, 21/13 on the x axis. From left to right: the bar labelled 1/1 is pale purple and reaches up to 1.0. The bar labelled 2/1 is gold and reaches up to 2.0. The bar labelled 3/2 is bright purple and reaches up to 1.5. The bar labelled 5/3 is dark purple and reaches up to 1.667. The bar labelled 8/5 is orange and reaches up to 1.6. The bar labelled 13/8 is turquoise and reaches to 1.625. The last bar, labelled 21/13 is bright blue, and reaches up to 1.615. These ratios are written in the centre of each bar. A dotted line stretches across the graph, at the level of 1.618033988749895... This is labelled with the symbol for Phi. A circle with a vertical line through the centre.

What is the next pair of numbers you could add to the graph above? What would be the value of this ratio?

The dotted line is labelled with the symbol Φ. This is the 21st letter of the Greek alphabet, Phi. In math, Phi represents a number that starts with 1.618033988749895… And goes on forever without repeating! That’s one reason Phi is an  irrational number .

Did you know? An irrational number is a real number that cannot be written as a simple fraction. For example, 1.5 can be written as 3÷2. But you can’t do that with Phi.  Pi  (3.14159265358…) is also an irrational number.

The Golden Ratio  

The Golden Ratio is not the same as Phi, but it’s close! The Golden Ratio is a relationship between two numbers that are next to each other in the Fibonacci sequence. When you divide the larger one by the smaller one, the answer is something close to Phi. The further you go along the Fibonacci Sequence, the closer the answers get to Phi. But the answer will never equal Phi exactly. That’s because Phi cannot be written as a fraction. It’s irrational!

The Golden Ratio can also be seen using two quantities, like the lengths of two line segments. Have a look at the lines below. The blue and green lines have the Golden Ratio. This is because the length of the longer blue line, divided by the shorter green line, is the same as the length of the two lines added together (shown in black) and divided by the blue line. In other words, two quantities have the Golden Ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

Shown is a colour illustration of line segments and a mathematical equation. At the top is a long black stripe labelled Line Segment. Below is a shorter blue stripe labelled Long Segment. To the right is an even shorter green stripe, labelled Short Segment. When placed end-to-end, the blue and green stripes equal the length of the black stripe. The equation is below this illustration. On the left, the words Long Segment in blue is divided by the words Short Segment in green. To the right is an equals sign. Next, the words Line Segment in black is divided by the words Long Segment in blue. This is followed by another equals sign. Next, 1+ the square root of 5 is divided by two. This is followed by another equals sign. To the right, the answer is 1.61803...

A Golden Rectangle works in a similar way. But the quantities are shapes rather than lines. Have a look at the diagram below. The rectangle has a long side of  a + b  and a short side of  a . This is the entire coloured area of the diagram.

Imagine cutting off a square section of this using one line. The square is shown in blue. Each side of its sides is equal to the shortest side of the original rectangle, or  a .

But look at the smaller, leftover rectangle shown in pink. This has the same ratio of side lengths as the original rectangle! Even though it’s smaller, it can be divided in the same way as the first.

Shown is a colour diagram of a rectangle divided into a pale purple square and a smaller pink rectangle. The top and left edges of the square are each labelled with a blue, lower case, italic a. The top edge of the smaller rectangle is labelled with a red, lower case, italic b. The entire bottom edge of the larger rectangle is labelled with a + b, in green italics.

The ratio between sides  a  and  b  is Φ or 1.61803… You can see this written as an equation below:

We can grow this pattern by adding a new, larger square to the long side (a + b) of the rectangle. This square, combined with the previous shapes, results in a new, larger rectangle. Do this again and again, and you can create a growing pattern, like the diagram below.

Shown is a black and white illustration of a rectangle divided into smaller squares and rectangles that get smaller as they move around the page, towards a spot in the bottom right quadrant. The largest rectangle is divided into many smaller shapes. The largest, on the left, is a square labelled with the number 34. To the right of the square is a vertical rectangle. This is divided into a square, labelled 21, and another, smaller, horizontal rectangle. The third rectangle is divided again. The square in the right is labelled 13. The vertical rectangle is further divided into a square labelled 8, and a horizontal rectangle that is divided again. The next square is labelled 5. Next to it, another vertical rectangle contains a square labelled 3 and a smaller horizontal rectangle, which, in turn, contains a square labelled 2. The smallest square is not labelled, but it looks like this pattern could continue, becoming smaller and smaller with each iteration.

How big would the next square be, to continue growing the pattern in the diagram above?

We can take the Golden Rectangle one step further by adding a line that forms a quarter circle in each square.

Have a look at the diagram below. The curved lines connect to form a spiral. This is called a  Fibonacci Spiral . Each square is also labelled with the length of its sides. These numbers are the same as in the Fibonacci Sequence!

Shown is a black and white illustration of a rectangle divided into smaller squares and rectangles, overlaid with a blue spiral line. The largest rectangle is divided into many smaller shapes. The largest, on the left, is a square labelled with the number 34. The blue line over it curves from the bottom left to the top right corner, in a quarter circle. To the right of the square is a vertical rectangle. This is divided into a square, labelled 21, and another, smaller, horizontal rectangle. The square labelled 21 is overlaid with another quarter circle, from the top left, to the bottom right corner. The third rectangle is divided again. The square on the right is labelled 13. It is overlaid with a curved blue line from the top right to the bottom left. The vertical rectangle is further divided into a square labelled 8, and a horizontal rectangle that is divided again. The blue line continues to curl across these shapes. The next square is labelled 5. Next to it, another vertical rectangle contains a square labelled 3 and a smaller horizontal rectangle, which, in turn, contains a square labelled 2. The blue line continues to curl smaller across these shapes. The smallest square is not labelled, but this is the point where the blue spiral ends in a tight curl. The pattern looks as if it could continue, dividing into smaller and smaller shapes, with the spiral becoming tighter and tighter.

The Golden ratio can also form a spiral (©2022 Let’s Talk Science).

Shown is an animated gif of a spiral growing with larger and larger squares of different colours. The first square is tiny and blue, with a curved white line from the bottom left to the top right corner. The second square appears above. It is much larger and the line curves from the bottom right to top left. The third square is larger again. It appears to the left of the rest, and the line curves from the top right to the bottom left. The fourth square appears below the others, with a line from top left to bottom right. The fifth square is orange, and appears on the right, with a line from the bottom left to the top right. The fifth square appears on top of the rest, in pink, with a line from the bottom right to the top left. The final square is so large it takes up more than half the page, and fills in all the space to the left of the rest. It is blue with a line curving from the top right to the bottom left. When all the squares are put together, the curved lines across them form a spiral. This spiral grows out from a tiny blank square in the bottom right corner of the page.

Fibonacci Spirals in Nature

Remember those flower petals? They help draw  pollinators  to the centre of the flower where the pollen is - like a bull’s eye. This is why many flowers have evolved to grow petals in a Fibonacci spiral around their centres. Each new petals grows about 137.5 degrees away from the last. This is 1 ÷ Phi x 360 (total degrees in the circle). Or you can imagine dividing a circle into two curved lines. The arc of the longer line and the arc of the shorter line have the golden ratio. This is called the  golden angle . In fact, if you  count all the petals on a flower , you will often find a Fibonacci number!

Shown are five colour photographs of different, single flowers, arranged in a row and labelled with their number of petals. The first flower has three wide, pointed white petals and three smaller green leaves. The second has five round, blueish purple petals around a small yellow centre. The third has eight almond-shaped petals that are dark pink near the centre and white at the tips. The fourth has 13 long, narrow yellow petals with curved ends. The fifth has bright long narrow, bright purple petals around a darker purple centre.

But it’s not just petals that follow this pattern. Other plant parts follow the Fibonacci Sequence too. Seeds need enough space to grow properly. Have a look at the sunflower below. The seeds are packed into the centre of the flower in a very familiar pattern!

Shown is a colour photograph of the centre of a sunflower, with a blue spiral superimposed on it. The flower has bright yellow petals. Its centre consists of tiny, pointed, deep yellow structures, densely packed into a circle. The spiral demonstrates that the tiny pointed structures are laid out in a spiral pattern.

The same pattern can be seen in pinecones and pineapples. If you take the time to count the spirals in each direction, you often find Fibonacci numbers!

Misconception Alert! Fibonacci Spirals and Golden Spirals are not the same. A Fibonacci spiral is made of squares that increase in size. But a Golden Spiral is made by nesting smaller and smaller Golden Rectangles within a large Golden Rectangle.

The Golden Ratio can be used with other shapes as well. It is possible to find golden ratios in patterns involving circles, triangles, pentagons and other shapes.

Shown is a diagram of intersecting triangles, pentagons, squares and circles with blue lines drawn over them. The largest triangle is acute, and contains seven other, smaller triangles. Its left outside edge is covered by a blue line, labelled 1.618. The blue line turns the corner and continues on its bottom edge, labelled 1. This triangle is divided into an isosceles triangle and a scalene triangle. The scalene triangle is further divided into another acute and another isosceles triangle. The blue line continues around the long, then the short edge of the acute triangle. This triangle is divided again, into another acute and another isosceles. The blue line continues along the base of the acute triangle, which is further divided into another acute and another isosceles. The blue line continues along this base, and the triangle is divided again. The blue line finishes as it turns a tight corner along the base of the smallest acute triangle. In total, the blue line forms a sort of spiral, with a series of acute angles and straight edges that become shorter and closer towards a point in the bottom right of the largest triangle. The largest pentagon is labelled 8. Its bottom edge is covered with a blue line. Inside that, a smaller pentagon is labelled 5 and the blue line continues along one of its edges. Inside this are smaller pentagons labelled 3 and 2, where the line continues along an edge of each. Two even smaller pentagons are unlabelled, but they follow the same pattern. All the segments of the blue line forms a spiral with obtuse angles and straight edges that become shorter and closer towards a point in the lower right of the largest pentagon. The largest square is labelled 8. A smaller one, butted up against it on the right, is labelled 5. A blue line is drawn from the top left corner of the large square, to the top left corner of the smaller square, forming a slope down to the right. Smaller and smaller squares, labelled 3, 2 and 1, follow the same pattern, and the blue line continues in a straight slope down to the smallest square, on the far right. The largest circle is labelled d=8. A blue line covers the upper left part of the circumference. Inside it, smaller circles are labelled 5, 3, 2 and 1. The blue line continues along part of the circumferences of each circle, forming a spiral. This curls to its smallest point in the top right of the largest circle.

So, plants do math! Pretty smart eh?

What number comes after 4181 in the sequence above? 6765

What is the next pair of numbers you could add to the graph above? What would be the value of this ratio? 34/21, 1.619

How big would the next square be, to continue growing the pattern in the diagram above? 55x55

The Golden Ratio: Is It Myth or Math?  (2021) This video (22:54 min.), by Be Smart, looks at the mathematical reality of the Golden Ratio, and some of the stories around it.

The Golden Ratio (why it is so irrational)  (2018) This video (15:12 min.), from Numberphile, uses flower seed distribution and fractional turns to show what happens numerically when Golden Ratio spirals form.

Rational, Irrational and Real Numbers  (2021) This video (4:35 min.) by Let’s Do Math, provides an overview of the differences between rational and irrational numbers.

Be Smart (2021).  The Golden Ratio: Is It Myth or Math?  YouTube.

Carney-Gies, F. (2023, August 9).  Fibonacci . Encyclopedia Britannica.

Cuemath. (2020, September 17).  Acharya Pingala .

The Editors of Encyclopedia Britannica. (2023, September 14).  Hindu-Arabic numerals . Encyclopedia Britannica.

Haglund, C. (2023, May 3).  Flowers & the Fibonacci Sequence . Montana Natural History Center.

Huffman, C. J. (n.d.).  Mathematical Treasure: Fibonacci's Liber Abaci . Mathematical Association of America.

Mann, A. (Nov 25, 2019).  Phi: The Golden Ratio .  LiveScience .

Math Is Fun (n.d.).  Nature, The Golden Ratio, and Fibonacci too...

Phyllotaxis (n.d.).  Fibonacci Numbers - Golden Angle . 

Reich, L. (2013, February 20).  Nature follows a number pattern called Fibonacci . Phys.org.

Wikipedia.  Pingala .

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3 Steps For Using The Golden Ratio To Create Masterful Paintings

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What is the Golden Ratio?

The golden ratio (also known as the golden section, and golden mean) is the ratio 1:0.62. Use it to divide lines and rectangles in an aesthetically pleasing way. In the above square A is 0.62 of the rectangle. Square B is 0.62 of square A. Square C is 0.62 of square B, and so on. It is also called the divine proportion, and golden number. It is a mathematical ratio that’s commonly found in nature, and can be used to create visually-pleasing compositions in your artwork.

Details: The Golden Ratio In Art

The golden ratio is a method that you can use to divide lines and rectangles in an aesthetically pleasing way. Architects use a very accurate golden ratio number, 0.62, when designing buildings. As an easier rule of thumb for your art, you can use a ratio of 3 to 5. Although not the exact 0.62 golden ratio, this is close enough for artists. This golden ratio has been used throughout history by artists to place points and lines of interest in their work.

In “ A Stroll in Xizhou” the houses on the street in the sunlight were casting interesting shadows across the road. I needed to divide the shadow areas and the sunlit areas into two different sizes to make them interesting. I ended up stopping the lit part of the street exactly 5 parts out of 8 in the horizontal direction – the golden ratio.

You may wonder if I measured this while I was painting? In actual fact I did not even think about the golden ratio while I was in the middle of the painting. I only discovered after I had finished that I had used the golden ratio everywhere! When I was painting the picture it just “felt right”. While you are starting out, you can measure this point to place key lines and points of interest, but later on it will become more intuitive and you will not have to think about it – much like all the other aspects of painting.

In this diagram you can see the horizontal shadow line was also placed at the golden ratio and so was the large figure to the left.

3 Steps To Apply The Golden Ratio In Your Paintings

• Divide the edge of your canvas into eight sections by halving it several times to create 8 divisions.

• Draw a line down the canvas at the third section from the left (or right).

• Draw a line across the canvas at the third section from the bottom  (or top).

• Place the focal point or focal area of your painting where the lines meet.

You can draw the lines at other 3:5 sections of your paintings to create different compositions.

Examples Of The Golden Ratio

Here are some old master paintings where you can clearly see they have used the golden ratio. The 3:5 golden ratio gives you a very pleasing division of your canvas. Use it to place your focal point, or focal area, as Sargent, Zaitsev, and Vermeer did here.

Learn more about using the golden ratio in your paintings.

To learn more about how to use the golden ratio, focal area, and for other composition and techniques, see the lessons in Workshop E of the Virtual Art Academy Apprentice Program.

Read more about space division in your paintings , and interlocking shapes in order to make your compositions more interesting and engaging for your viewers.

See also Wikipedia: Golden Ratio

Thank you for taking the time to read this article. I hope you find it useful. If you would like to get free painting tips by email, please sign up for my free tips newsletter .

If you are interested in a structured approach for learning how to paint, take a look at my online painting classes .

Happy painting!

Barry John Raybould Virtual Art Academy

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Home / Design / How To Use The Golden Ratio in Graphic Design

How To Use The Golden Ratio in Graphic Design

The Golden Ratio pattern is a mathematical ratio commonly found in nature. In graphic design, it instantly attracts viewers because of its symmetry and visual appeal. Read this short guide to know what the golden ratio is, and how you can use it in graphic design!

The Golden Ratio Pattern: From The Pyramids of Giza To Apple Inc.

Hyped or extraordinary: what’s golden ratio in graphic design.

The ratio’s numeric value is approximately 1.618. The Greek alphabet Phi φ symbolizes The Golden Ration. The Golden Ratio is a crucial element of design because it achieves harmonization in nature and even within our bodies. That’s why when you look at images online, you can spot how different brands use the Golden Ratio in graphic design .

The Golden Ratio Pattern In and Around Us

• This magical ratio exists in flowers, leaves, and even within us… in the shape of our skulls!

• In architecture, namely, the studies of the Pyramids of Giza (one of the Seven Wonders of The World) have revealed that their design follows the Golden Ratio pattern.

Related: How to Change the Aspect Ratio of Your iMovie Project

• In the world of art, Leonardo Da Vinci’s iconic masterpiece, The Mona Lisa, is painted to the ratio’s proportions.

• Similarly, the golden ratio is also in Apple’s graphic design, which has championed its use within its brand logo. This itself is a subtle nod to the Most Beautiful Number in The Universe.

The Fibonacci Sequence

Wondering what the circles are around the Apple logo? What you’re seeing is the work of mathematician Leonardo Fibonacci, who devised a sequence of numbers in which each member is the sum of the previous two. These “spiral geometries” are best approximated through the golden ratio, and run from 1,1,2,3,5,8,13,21,34 to infinity. Therefore, as it turns out, there is never-ending symmetry in nature!

What Do Snails and the Apple Logo Have in Common?

You guessed right: the Fibonacci Sequence!

The shell of a snail is as perfectly approximated to the Golden Ratio in nature as the Apple logo is in its proportions.

via wereworlfsmurf.tumblr.com

The shell that you see on a snail is a self-similar object – repeating itself in the same way, but smaller and smaller, and at all scales. Likewise, Apple has used these repetitive spirals in its branding to achieve the same symmetry.

via Edutopia

Using the Fibonacci Sequence and the Golden Ratio together is called The Golden Spiral, most famously used by Salvador Dali in The Sacrament of the Last Supper.

How To Design Keeping The Golden Ratio Pattern in Mind

Before we deep dive into the how of using the golden ratio, let’s first take a short look at the why of using the golden ratio in graphic design.

3 Ways Using the Golden Ratio in Graphic Design Helps Your Images:

• Faster Recognition: Prominent research and studies posit that when the golden ratio is a fundamental element of design, the human eye registers it much quicker than any other design. This is the first call to effective design – attracting eyeballs.

• Visual Balance: What makes you linger on one design and scroll past the next? The answer is consistent – it’s the golden ratio! We are hardwired to prefer images with a perfect harmony of elements. In summary, the golden ratio in graphic design is what makes us stay longer on an image.

• Perception of Beauty: The application of the golden ratio to gauge symmetry and the alignment of human faces and bodies is well known. What happens when we include this perfect ratio in our designs? The audience is more likely to engage with our brands because of the perception of beauty mirrored in our graphic designs.

The Golden Ratio In Graphic Design: How To Incorporate in Your Process

Think of your brand’s needs when you start designing using the Fibonacci Sequence and the Golden Ratio. Perhaps you want to re-brand your logo for scaling your company? Or you want a more effective logomark that will instantly connect with your brand logo? Either way, we have you covered!

3 Ways You Can Use the Golden Ratio:

• Typography: The golden ratio is not exclusive to media! You can just as effectively use it to make your type more visually appealing. Moreover, the ratio can help you decide what size font to use for headers, on your landing page, or even a feed advertisement.

Related: How to Use Geometric Patterns Creatively in Graphic Design

• Cropping and Resizing Images: When you crop images to fit your design, canceling out the negative space is easy by cutting out white borders. How do you know that your resized image carries the same visual attractiveness? We recommend overlaying the Golden Spiral on your image, like below, with the focal point in the middle of the spiral.

• TIP: Start with this Golden Ratio Generator!
• Brand Logo or Logomark: You can turn to the Golden Ratio whenever you’re stuck and in need of some inspiration. Furthermore, its perfect measurements can guide you on the size and alignment of your logo or logomark. For instance, brands like Apple, Twitter, and Pepsi have successfully done this.

There is no one-size-fits-all when it comes to graphic design – to each their own! However, by using the golden ratio in graphic design, you’ll be following in Da Vinci’s, Dali’s, and Apple’s footsteps. Who are all recognized connoisseurs of art and design.

Finally, to get you started with the Golden Ratio, use this template to create stunning designs on Simplified!

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• Golden Ratio

The Golden Ratio

The Golden Ratio, in mathematics, also known as Golden section, divine proportion, or Golden mean, is an irrational number, which is denoted by the Greek letter “phi” or “φ”. The Golden Ratio or Golden number is defined as the ratio of a line segment, which is cut into two pieces of unequal lengths, where the ratio of the whole segment to the longest segment is equal to the ratio of the longer segment to the shorter segment. The Golden ratio value or golden number is the irrational number \[\frac{(1+\sqrt{5})}{2}\]  which is approximately 1.618. 

History of Golden Ratio

The history of the Golden ratio can be traced back to ancient times, where Greek mathematicians like Euclid and Pythagoras spent endless hours researching the equation and its properties. The Greek mathematician Euclid mentions the Golden ratio in the elements, where he implemented some propositions of the ratio. He used to call it the extreme and mean ratio. 

The Golden section frequently appeared in geometrical calculations, including the Pentagrams and Pentagons. The Ancient mathematician Hippasus of 5th century B.C. discovered that the Golden number or divine proportion was neither a whole number nor a fraction, which surprised the Pythagoreans. 

Over the past decades, many mathematicians have studied the Golden number’s importance, uses, and properties and have applied it to many mathematical formulas and calculations. In the 18th century, mathematicians, including Abraham de Moivre, Daniel Bernoulli, and Leonhard Euler, used the Golden ratio formula to discover the value of Fibonacci numbers. In the 1960s, Steve Baer discovered the Zome construction system based on the Golden ratio formula. 

Applications And Usage of Golden Section

The Golden section can be applied in various fields of studies starting from art and architecture to nature. Below are some of the most important uses of the divine proportion.

Art: Most painters and artists used the Golden section in their artistic masterpieces in the ancient era. They used the ratio to add beauty and make their art in the perfect proportion. Mathematicians like Luca Pacioli used the Golden section to provide pleasing and harmonious proportions for paintings. He also found Catholic religious significance in the ratio, for which he also titled the paintings after the ratio. 

Another great artist, Leonardo da Vinci also adopted Pacioli’s Golden section in his paintings to bring out a perfect proportion in them. Leonardo da Vinci’s famous painting, the Mona Lisa, is based on the Golden section and is considered the most beautiful painting having a perfect facial proportion. 

Designs and Books: In the books of early ages, one can find the divine proportion, which is in the ratio 5:3, and is scarce. We can find the divine proportion in many ancient manuscripts and incunables, which were printed in European countries. Even today, you can also find the golden section in many designs, including playing cards, posters, postcards, light switches, and televisions. 

Music: The golden section also plays a crucial role in the music industry, and many famous music composers and singers use it in their musical masterpieces. Famous French composer Erik Satie used the golden section in a few of his songs, including the Sonneries de la Rose. 

Nature: We can also observe the golden section in various aspects of nature. According to Johannes Kepler, the Golden ratio in nature can be seen in the propagation of plants and progenitive acts of animals.

Many other scientists and researchers have found evidence of the golden section in natural activities claiming it to be a universal law of nature.  

Apart from the fields mentioned above, the golden section is also used to study the perfect facial proportion. According to scientists, persons with a golden ratio face are considered more beautiful and appealing than others. They consider that there should be a proportionate gap between all the facial aspects to make a person look appealing. 

Golden Ratio Calculator

The golden ratio calculator is a valuable yet straightforward calculation method that helps you identify the shorter segment, the longer segment, and the combined value of the line segment with the help of a simple formula. If we consider a line segment with the longer segment a and shorter segment b, the golden section can be calculated by the formula: (a+b)/a = a/b. 

You can easily calculate the golden ratio of any two quantities by hand; here are the steps:

First, take a greater side or value and mark it as “a”.

Again take a smaller side or value and mark it as “b”.

Now, input all the values as per the formula; (a+b)/a = a/b.

Calculate a+b and divide the result by the value of a.

Calculate a/b.

If the answer is approximately equal to 1.618, then your quantities are in golden proportion. 

What is the Golden Ratio Rectangle?

While studying the concepts of the golden section, we frequently come across the term golden ratio rectangle, but what is it? Let’s find out. A golden ratio rectangle or golden rectangle is a rectangle whose length is denoted by a+b and width is denoted by a. Here a is the longer side, and b is the shorter side. It is used in art and architectural designs to bring out perfect proportions in constructions and paintings.   

Facts And Examples of Golden Ratio

Above, we discussed the golden ratio, its application, and calculation; now, let’s discuss some of the golden ratio examples and go through some amazing facts about the golden ratio. 

Below are some golden ratio examples that will help you understand the concept of the golden number.

You can find the pattern of the golden section in architectural wonders, such as The Great Pyramid of Giza.

You can also find the golden section in the famous Mona Lisa painting by Leonardo da Vinci. 

You can also find the golden section in the petals of flowers. The petals of a flower always follow the Fibonacci series, which is closely related to the golden section.

The galaxy’s spiral shape is an excellent example of the golden section, where each spiral arm is approximately 12 degrees.

(Image Will be Updated Soon)

Now, here are some fantastic and astonishing facts about the golden ratio.

The golden ratio has many names, including the golden section, golden proportion, divine proportion, medial section, extreme, and mean ratio, etc.

The golden section occurs only when the formula of an equation is equal to the number phi, which is equal to 1.618.

We can find the golden section in things around us, and many forms of nature also prove that the golden section is a universal law.

The value of the golden section is a continued fraction, and therefore it is denoted by the “phi” symbol. 

FAQs on Golden Ratio

Q1. What is a Golden Rectangle?

Answer: The golden rectangle is actually a rectangle that has a length of a+b and a width of a. This rectangle is most commonly observed in art, as it has also been believed that it's the most captivating to the eye of all such rectangles. There is also a golden rectangle calculator which is a convenient tool to find the golden rectangle instead of working it manually. It also has its presence as the golden ratio in nature as well as the golden ratio in architecture. In other words, the golden ratio is observed in various forms of architecture and some concepts of nature, such as in the arrangement of leaves in some trees or decorative plants. The golden proportion is even spotted in regular pentagons.

Q2. How Do We Use the Golden Ratio to Improve Designs?

Answer: You can spot the Golden Ratio when you divide a line into two parts and the longer part (x) divided by the smaller part (y) is equivalent to the sum of (x) + (y) divided by (x), which both equal 1.618. This formula will enable us to create shapes, signboards, logos, layouts, and more.

Considering this idea, we can also create a golden rectangle. Take a square and multiply its one side by 1.618 to obtain a new shape: i.e. a rectangle with well-balanced proportions.

Q3. What is a Beauty Ratio?

Answer: A beauty ratio is actually the golden ratio in beauty. Also known as the golden face ratio, it means the ideal outcome—as described by the golden ratio—is approximately 1.6, which implies that a beautiful person's face is about 1 ½ times longer than it is wide. This also suggests that if the numbers are matching or equal, a person is considered more beautiful.

Q4. Define the golden ratio.

In mathematics, the golden ratio or golden number is an irrational number denoted by the Greek symbol “phi” or “φ.” It is also known as the golden section, golden proportion, medial section, and divine proportion. The value of the golden section is equal to 1.618. It is a continued fraction and therefore is denoted by the symbol “phi”. The golden section has many applications and can be found in many aspects of nature. Many renowned artists and mathematicians have used the ratio in their Works.

Q5. What is a golden rectangle? How to calculate the golden section?

A golden rectangle, also known as the golden ratio rectangle, is a rectangle where the longer part of a side is denoted by the letter “a” and the shorter part of the same side is denoted by the letter “b”. Hence, in the golden rectangle, the length of the side is denoted by a+b, and the width is denoted by a. If we find the ratio of the length to its width, we obtain the golden section. It is used in many architectural marvels by engineers and designers. To calculate the golden section, we take two line segments, where the longer segment of a side is denoted by a, and the shorter segment of the same is denoted by b. Now, the formula for the golden section is (a+b)/a = a/b. Now, we have to place all the values in their respective positions. Solving the equation, you will find the result equal to the golden number or “phi”.

Golden Ratio Calculator

Table of contents

The golden ratio calculator will calculate the length of the parts into which you need to divide a segment to obtain the golden ratio . Before we move on to actually computing the golden ratio, let's discuss what the golden ratio is all about. In what follows, you can find all the knowledge you need!

You can also check out the proportion calculator if you want to learn about ratios in general.

Golden ratio definition

The golden ratio (also known as the golden section or golden proportion ) arises when a segment is divided into two parts — the proportion of the longer to the shorter part must be the same as the proportion of the whole segment to the longer part. That is, if the longer part has length a a a and the shorter part has length b b b , the golden ratio formula reads:

To compute the value of the golden ratio, you need to solve the equation above for a / b a/b a / b . It's convenient to rearrange it as

Thus, in the end, we only need to solve for x x x the quadratic equation x 2 − x − 1 = 0 x^2-x-1=0 x 2 − x − 1 = 0 . We do this by standard methods and discover that the value of the golden ratio is equal to 1 2 ( 1 + 5 ) \frac 12 (1+\sqrt{5}) 2 1 ​ ( 1 + 5 ​ ) , which is approximately 1.61803398875... 1.61803398875... 1.61803398875... . This number is often denoted by the Greek letter ϕ \phi ϕ .

🙋 The golden ratio 1.618... 1.618... 1.618... coincides with the limit of the ratio of consecutive Fibonacci numbers! Is that magic ? Learn more with the Fibonacci sequence calculator !

We now know what the golden ration is and how to compute its value, so let's discuss how to verify if some two given lengths obey this divine proportion.

How do I check to see if two segments are in the golden ratio?

Here are the step-by-step instructions to help you figure out if two segments are in a golden ratio:

• Find the length of the longer segment and label it a .
• Find the length of the shorter segment and label it b .
• Compute a/b .
• If the proportion is (approximately) equal to 1.618 , your segments are in golden proportion.

You can also use Omni's golden ratio calculator to do the job. Although any ratio calculator can help you with that, our golden ratio calculator deals with this issue specifically, so you won't find a better tool!

How to use this golden ratio calculator?

Omni's golden ratio calculator couldn't be any more user-friendly and straightforward. It has three fields , corresponding to the three lengths that appear in the formula for golden proportion. And you only need to enter one of them for the remaining two to be computed automatically. Isn't that terrific?

Golden rectangle

The golden rectangle is a rectangle whose side lengths obey the golden ratio, i.e., the proportion of its length to width is 1.618 1.618 1.618 . This rectangle is often seen in art, as it is believed to be the most pleasing to the human eye of all rectangles. The golden rectangle calculator is a convenient way to find the sides of a golden rectangle instead of working them out by hand.

Why is the golden ratio important?

The golden ratio has always had particular relevance in science and art thanks to its properties and appearance. Talking about math:

• A golden rectangle can be split into two smaller golden rectangles (it maintains its proportions).
• The golden ratio deeply correlates with the number 5 . This number appears in its definition ( φ = (1 + √5)/2 ) and the pentagon as the ratio between diagonal and side.

In arts, the golden ratio appeared more recently: Dalí, for example, used this ratio in many of its works.

Where can I find the golden ratio in nature?

Many historical and contemporary sources claim that the golden ratio is rather ubiquitous in nature. Some examples are:

• The growth pattern of leaves ;
• The geometrical surfaces of some vegetables and shells ;
• The proportions of the bones of some animals .

However, while we can't deny the presence of geometrical patterns in nature, we can't confirm the exactness of the proportions of the examples above: some present huge variations, while others only approximate the golden ratio.

What is the golden ratio?

The golden ratio is a ratio between two quantities that we can also find when we compute the ratio between the sum of these quantities and the greater of the two . Numerically speaking, the numbers a and b are in the golden ratio if:

a/b = (a + b)/a

The value of this ratio is approximately equal to 1.618 .

What is the length of the sides of a golden rectangle with diagonal 1?

The sides of a golden rectangle with diagonal d = 1 are a = 0.850651 and b = 0.525731 . To find these results:

Use the Pythagorean theorem to find the length of the side b as a function of a :

b = √(1 - a²) .

Compute the length of the side a knowing that a/b = φ :

a/b = φ a/√(1 - a²) = φ a = √(φ²/(1 + φ²)) = 0.850651

Compute the length of side b with the following formula:

b = a/φ = 0.525731

Longer section (a)

Shorter section (b)

Whole (a + b)

Title : Ratios and the Golden Ratio

Audience : High School Geometry

Length of Lesson : two 50-minute periods  

http://hs.houstonisd.org/debakeyhs/Lessons/ratioprocedures.html

http://www.thirteen.org/edonline/nttidb/lessons/dn/golddn.html

I.           Performance or learner outcomes

                         The student will be able to:

                      - Calculate the Golden Ratio                         - Find examples of the Golden Ratio by measuring parts of the body                         - Find other natural examples of the Golden Ratio                         - Apply knowledge of these ratios to draw a body to scale

II.          Overview

Teacher will initiate a brief review of ratios.   Students will explore ratios of body measurements and their relation to the Golden Ratio and Fibonacci Numbers.   They will hunt for other examples of Golden Ratios.   They will apply their knowledge of the human body to draw a sketch using the ratios.

III.         Resources, materials and supplies needed

                        3x5 index cards

                        measuring tape (fully flexible to measure around bodies)

                                    or alternatively, string and meter sticks

                        calculators

                        overhead projector and blank transparencies

                        large sheets of paper for each student

                        Polaroid cameras

                        Basket with papers containing various heights

IV.         Supplementary materials, handouts.

                        Student Instructions/ Data Sheet, see Appendix A

V.          Standards

            TEKS

§111.34.(c) Geometric patterns: knowledge and skills and

performance descriptions.    The student identifies, analyzes, and describes patterns that emerge from two- and three-dimensional geometric figures.

§111.34 (f) Similarity and the geometry of shape: knowledge and skills and performance descriptions. The student applies the concepts of similarity to justify properties of figures and solve problems.

Teacher does

Let’s review ratios.

Pass out 3x5 index cards and a ruler.

Today we are going to learn about proportions of the human body.

Let students try out some of these examples.

Probing Questions

If the lengths of a right triangle ABC are 3,4,5 and we have discovered a similar triangle DEF with the ratio of ABC to DEF being 1/25 what are the lengths of the sides of DEF?

Can anyone tell me the ratio of the longer side to the shorter side of the index cards?

If I wanted to shrink the index card by 60%, what would the new measurements be?   Would the ratio of the sides be the same?

Has anyone ever noticed specific properties about the measurements of the human body?

Student Does

75, 100, 125

yes, the ratio would still be the same.

Various answers: possibly that the length of forearm= length of foot, arm span= height, etc.

Pass out page where they can fill in measurements of their bodies.   They should be in groups of two, helping to measure each other.

Each student does a variety of measurements of their bodies and fills out the sheet.   (see attachment).

Teacher does

Tell the students this ratio is called the Golden Ratio or phi.   It is prevalent in nature and art.   It is an irrational number   (1+ sqrt5)/2 or   1.61803399.   The Golden Ratio is thought to be very aesthetically pleasing.

Can you make any conjectures or come up with some theories about these ratios?

What have we been learning about in the past few days?

Can I have a volunteer come to the board and write the Fibonacci Numbers?

Now, looking at these numbers can we find any thing close to the ratio of body proportions we found?

Lets think back to the 3x5 note card.   Doesn’t this ratio seem close to the Golden Ratio?   Do you think this is on purpose?   Explore board game rectangles, etc at home to see how frequently the Golden Ratio is used.

Student Does

One student from each pair puts the results of their ratio calculations on the overhead.

Students each calculate the averages.

Hopefully, the students will find that the ratios are all near 1.6.

The Fibonacci Numbers.

1,1,2,3,5,8,13,21…

class helps out and the sequence continues.

Students have a few minutes to calculate ratios, and hopefully will realize that the ratio of the (n+1)th number over the nth number approaches the ratio as n gets larger.

On transparency, students calculate ratios of consecutive Fibonacci Numbers and they are shown to move progressively towards phi.

Students measure and make a list and sketch of any items they find that are in the golden ratio using measuring tape, etc.

Polaroid cameras can be used to take pictures of items.   These pictures are later shown to the class and they explain them.

If time does not allow in class, this should be continued for homework.   Using paper pencil, ruler and some imagination, consider the golden ratios found in the human body.   Draw a body to scale.   A basket will be passed around, giving heights of people.   The assignment is to use these ratios to approximate a body shape/size.   Students must scale down the body size to fit on the piece of paper.   Therefore, two ratios will be applied.   The drawing should include the ratio of the actual height of the person to the scaled down model.   Appendix A

Name _________________________                        Date _____________________

Take the following measurements

B=         the height from top of head to bottom of feet

N=       Navel height from the floor to the naval of each person in the group

F=        the length of an index finger

K=        the distance form the big knuckle in the "middle" of the index finger to the finger tip

L=        the length of a leg from hip joint to the floor

H=       the distance from the hip joint to the knee of the same leg measured above

A=        the length of an arm from shoulder to the fingertips

E=         the distance from the elbow to the fingertips of the same arm above

C=       the distance from the top of the head to the chin

Y=        the distance from the center of the eyes to the chin

M=       the circumference of the head and call it M.

I=          the circumference of the neck and call it I.

_____________

­­­­_____________

Calculate the following ratios:

B/N:                  _____________

F/K:                  _____________

L/H:                  _____________

A/E:                  _____________

C/Y:                  _____________

M/I:                   _____________

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The Golden Ratio

• Try this next
• Think higher
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and the human body

This exercise is divided into 3 parts:

A. The golden ratio

Distance from the ground to your belly button

Distance from your belly button to the top of your head

Distance from the ground to your knees

Distances A, B and C

Length of your hand

Distance from your wrist to your elbow

Now calculate the following ratios:

Distance from the ground to your belly button / Distance from your belly button to the top of your head

Distance from the ground to your belly button / Distance from the ground to your knees

Distance C / Distance B

Distance B / Distance A

Distance from your wrist to your elbow / Length of your hand

Write all your results on the following table:

Can you see anything special about these ratios?

B. The fibonacci sequence

Now look at the following sequence of numbers:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...

The following number is the sum of the previous two. This is Fibonacci's sequence.

Now do the following ratios on a calculator and give answers in non-fraction numbers:

As you go on and on dividing a number in the sequence by the previous number you get closer and closer to the number you discovered in the first part of the exercise, phi = $\phi$ = 1.6180339887498948482.

C. The golden rectangle

We can also draw a rectangle with the fibonacci number's ratio. From this rectangle we can then derive interesting shapes.

First colour in two 1x1 squares on a piece of squared paper:

Then draw a 2x2 square on top of this one:

Then draw a 3x3 square to the right of these:

Then draw a 5x5 square under these:

Then draw a 8x8 square to the left of these:

Then draw a 13x13 square on top of these:

We could go on like this forever, making bigger and bigger rectangles in which the ratio of length/ width gets closer and closer to the Fibonacci number.

Then place the compass tip on the bottom left corner of the 2x2 square and draw an arc like this:

Then place the compass tip on the left hand, top corner of the 3x3 square and do the same:

Do the same for the other three squares to obtain:

This shape is widely found in nature, can you find any other examples?

The Golden Ratio: Phi, 1.618

Golden Ratio, Phi, 1.618, and Fibonacci in Math, Nature, Art, Design, Beauty and the Face. One source with over 100 articles and latest findings.

The Human Body and the Golden Ratio

May 31, 2012 by Gary Meisner 62 Comments

The human body is based on Phi and 5.

The human body illustrates the Golden Section or Divine Proportion. We’ll use the golden ratio building blocks developed on the Life page again for each line segment:

The Divine Proportion in the Body

• The white line is the body’s height.
• The blue line, a golden section of the white line, defines the distance from the head to the finger tips.
• The yellow line, a golden section of the blue line, defines the distance from the head to the navel and the elbows.
• The green line, a golden section of the yellow line, defines the distance from the head to the pectorals and inside top of the arms, the width of the shoulders, the length of the forearm and the shin bone.
• The magenta line, a golden section of the green line, defines the distance from the head to the base of the skull and the width of the abdomen. The sectioned portions of the magenta line determine the position of the nose and the hairline.

Although not shown, the golden section of the magenta line (also the short section of the green line) defines the width of the head and half the width of the chest and the hips.

The Human Body is based on patterns of 5, which is the basis for Phi as well

Another interesting relationship of golden section to the design of the human body is that there are:

• 5 appendages to the torso, in the arms, leg and head.
• 5 appendages on each of these, in the fingers and toes
• 5 openings on the face.
• 5 sense organs for sight, sound, touch, taste and smell.

The golden section in turn, is also based on 5, as the number phi, or 1.6180339…, is computed using 5’s, as follows:

5 ^ .5 * .5 + .5 = Phi

In this mathematical construction “5 ^ .5” means “5 raised to the 1/2 power,” which is the square root of 5, which is then multiplied by .5 and to which .5 is then added.

August 29, 2012 at 1:41 pm

Interesting.

April 18, 2016 at 7:11 pm

I have used this ” GOLDEN RATIO ” in Dental Technology

January 8, 2018 at 10:37 pm

Me too Aaron 😀

November 21, 2016 at 11:45 pm

does anyone have any more information about the relationship phi and the human body? is there any books specifically about it? because i am currently doing an internal assessment ( a kind of research) and my topic is the relationship of phi/golden ratio and our human body 😀 ? thank you all

November 22, 2016 at 12:31 am

April 19, 2019 at 6:49 pm

Does anyone have or know of any website that I can get info. from abut the golden ratio in relation to the human body?

October 9, 2021 at 8:33 pm

What is the connection of Hermes to the Golden ratio?

February 12, 2022 at 6:34 am

Hello, I’m also doing an internal evaluation on this aspect. Can I borrow your topic for reference? I don’t have any ideas for choosing the topic now.

October 31, 2022 at 9:08 pm

ok but how does this affect LeBrons legacy?

August 29, 2012 at 9:02 pm

August 30, 2012 at 10:25 pm

My recent overview of this website has lead me to wonder if the human heartbeat has a direct corelation to phi. Perhaps in the measured longevity of the beat as well as the actual sound pattern.

March 6, 2013 at 3:24 pm

Interesting

March 2, 2014 at 1:28 pm

You have a point there.

December 30, 2015 at 6:30 am

You tube. I forget the name of the vid … Sacred geometry from memory, longish video and dude is a little full of himself and seems like wishful rubbish but in the end demonstrates interesting discoveries culminating in, seemingly, wonderous connection between his discoveries an the shape of the human heart.

December 30, 2015 at 6:32 am

. I found that vid to be an interesting watch anyways.

July 31, 2019 at 1:26 am

The Constance of our heartbeat is Pi, which has a correlation to the golden mean.

October 31, 2012 at 10:05 am

very good nice

December 8, 2012 at 11:38 am

everything is in mathematics – example the human body

January 7, 2013 at 5:10 pm

That is freaky in a cool way

December 13, 2013 at 1:48 pm

January 27, 2013 at 3:35 am

VERY VERY COOL!!!

February 17, 2013 at 5:37 pm

It strikes me so very interesting that as a young artist I was already learning the proportions of the human body so that I could draw a reasonably realistic figure, but in my case I learned the proportions from sources which used a more general fraction than the detailed decimal number shown in this site–that is, from books and teachers all the way back to grade school (and then, after going to the Fox Lane Junior High School in Upstate N.Y. and Long Island City High School in Queens, N.Y., I attended the Pratt Institute Art School for both my bachelor’s and master’s degrees and all the way through we had six-hour drawing classes each week and drew from nude models).

For example, when it comes to limbs, it was this way: The lower arm or forearm is two-thirds the length of the upper arm, which is longest; the hand (palm plus longest finger) is two-thirds the length of the forearm; each part of each finger, from longest to shortest, is two-thirds the length of each segment of the part of the finger before it, starting from where the finger is attached to the palm. This two-thirds proportioning is also applied to the feet, running from the upper leg bone to the lower leg bone to the foot. And, the artist generally uses the head of the individual to describe his or her height, although the basic general height of a generalized person is eight heads tall.

That’s why the “phi” and “fibonacci” as well as the “golden mean” caught my attention at this site. Actually, I originally set out to find out how to figure out the exact length of each limb (so I could get accurate lengths for shirt sleeves and pants), and that’s how I and this site crossed paths! You have to remember, too, that the artist does not stop to do mathematical calculations–the artist simply uses his sharp trained eyes, and so two-thirds is much easier to determine with the eyes than 1.61804 or 61.8%. By the way, the fraction two-thirds reduced to a decimal works out to .66666… or 66%.

Still, the artist is not viewing decimals; the artist views relationships through visual determination, and note, too, that art teachers or drawing instructors are always urging their student-artistes to exaggerate both the sizes of the body parts and the angles of a model’s poses! Meanwhile, the artist is certainly aware of the “golden proportion”, as it is named here. Ah! wonder of wonders, miracle of miracles!!! For li’l ole me (I just turned 65 on May 5th), ’twas once upon a time and long ago!

September 4, 2015 at 8:32 am

Oh wow, Thank you for your comment. Your comment is made this page even better!

February 18, 2022 at 12:32 pm

That is a long comment… it took me a while to read 😀 Thanks for your input. It opened a new perspective for me. Being an artist seems cool and your mathematical / artist insight added to the magic of the article. Keep it up honey!!!!

September 16, 2013 at 9:40 am

i like it because it has a lot of information.

November 17, 2013 at 8:39 am

Absolutely brilliant article. “In the beginning was the word, and the word was God” is referring to what I believe to be the word = sound = vibration. Have you seen the videos of sand on a speaker plate forming intricate patterns from the specific tunings of the sound? The beginning of the universe was formed from vibration which organizes matter into patterns. Ancient cultures knew this.

Pythagoras would have you fast 40 days on water just to enter his Pythagorean academy. He would then give you a “sacred meal” known as Pulse (as mentioned in Daniel 1:12 in the bible) he referred to it as “the meal of hercules” it was a sprouted fruit nut grain meal that was prepared to the phi ratio. ancient cutlures knew that food prepared in this way was perfect for the body.

March 2, 2014 at 1:24 pm

Can anyone tell me where on the human body can be found the exact golden ratio point? Would be at the heart?

April 3, 2014 at 3:05 am

I must say that the common believe in the five senses of the human body is, in fact, not true. We have more than 5 senses (and I’m not referring to the paranormal “eye” which some people believe in).

We have, for example, the sense of temperature, which is not the same as touch. The sense of pain is somehow related to touch but not quite the same. The sense of pressure. The sense of proprioception (which makes you able to know where your body parts are while closing your eyes). The sense of balance. …. Senses are, in fact, the human body taking information about the enviroment and processing this. The 5 5 5 5 thing is just mere coïncidence, or in other words, searching for something that is not there.

April 6, 2014 at 10:12 pm

Good point on human senses. The page has been corrected to say “five sense organs” rather than “five senses” to make it accurate. How do you determine what is coincidence and what is not? It’s possible to search for relationships that do not exist, but also possible to chose to dismiss those that do. Our underlying beliefs strongly influence how we see the evidence.

August 16, 2016 at 3:38 pm

Is the stomach not a sense organ? Hunger, nausea, connection to others, nervousness etc. Are all felt in the stomach.

Your lungs sense pressure change and humidity.

August 16, 2016 at 8:54 pm

Yes, that’s true. I see that the traditional list of five senses has now been expanded to as many as twenty-one. See http://www.todayifoundout.com/index.php/2010/07/humans-have-a-lot-more-than-five-senses/ .

July 3, 2017 at 12:44 am

thats amaZING

August 21, 2014 at 1:18 pm

For as long as I’ve been researching the Golden Section and related phenomenon- its still a bit of a hurdle to expect an absolute (even a proportional one) to occur in all humans. Even described simply- any pairing of normal human beings– with two eyes, two arms, two legs, nose, ears, mouth etc etc etc– seldom look the same. The great diversity of people on earth who belong to the same species is amazing. As much as I hate to ignore my intuition and numerous spiritual experiences, I can’t help but to desire a formula- at the very least, a guideline within which phi would occur unerringly. I doubt that’s going to happen, at least not within my current mathematical abilities- but in the meantime– if your trust your eyes as well as your math– check out the “test” I did in the video posted above. Not what I expected– but still fascinating.

August 25, 2014 at 8:12 pm

Great video! Please share more of your work here. One exception regarding your conclusions: See the Birth of Venus on the Botticelli page as analyzed in high resolution. I don’t think anyone takes the position that all humans conform to the golden ratio in all their proportions. It’s just the proportion that seems to appear with frequency and that is often related to perceptions of beauty.

August 25, 2014 at 10:59 pm

Thanks Gary! To be honest- I started off expecting to get a lot more yeses than nos- but felt I had to share the result one way or another. The final result being so close to 1.6:1 (even if not in the desired direction) was an odd surprise though. About beauty– often in the eye of the beholder– I’d be curious to hear from others, but in many cases (Lindsay Lohan for one) it seemed like those bodies which did conform to the Golden Ratio had the navel too high for my tastes– an odd observation I know– but after going through so many pics, couldn’t help but notice. Also- as the type of photos available tended to be celebs and professional models- I couldn’t help but wonder about different races and- shall we say– less “fit” family lines.

I actually found this after I had completed the video, but if any one else is interested, this study actually came to the opposite conclusion as I did: http://www.fq.math.ca/Scanned/17-4/davis-a.pdf I will definitely share more of my research in a future video- I just feel the need to apologize ahead of time for the 1998 slideshow tech level! 😉

September 30, 2014 at 11:37 pm

AWESOME. VERY INFORMATIVE.

November 11, 2014 at 7:00 am

December 8, 2014 at 9:42 pm

Interesting.Have to learn it

February 6, 2015 at 9:16 am

Way cool God’s opening up a new realization and inspiration for us to find that everything He designed can be reduced to numbers (mathematics – the universal language); even His word. it’s all going to end in PERFECT BEAUTY, which is HIM! 🙂 If this piques your interest, read Bonnie Gaunt’s book, Jesus Christ and the Number of His Name; The Amazing Number Code in the Bible; also Theomatics’ by Lucas and Washburn. God bless

December 29, 2015 at 7:40 pm

So…. you’re a believer Dawn???????? Just wondering…. cuz that’s way cool, I’m a believer, too!!!!!!!!!!! 🙂

February 16, 2015 at 2:26 am

this is really cool

February 27, 2016 at 12:43 pm

I like the way of the mathematical instructions are given.great Job indeed!!!!!!!!

April 5, 2016 at 12:11 pm

April 5, 2016 at 12:15 pm

this nimble artical was very revealing.

June 1, 2016 at 6:05 am

The golden ratio appears so often in nature so often eg Ammenites,flower petals, some tree species etc etc that it has to be more than a mere coincidence….God had a scientific calculater. FACT!

September 29, 2016 at 1:43 am

When I was younger in GT class, I think like 5th grade actually, we did this project on the golden ratio and we measured everyone in the class. I turned out to be the only one that had the golden ratio. Our teacher also had us see how many letters are in each part of our names. Mine is Jaime Pablo Lopez which is 5, 5, 5. So we were all trippin by then. And I I don’t know some wierd stuff has been going down in my life since then, I mean like not anything crazy but ya know, I just always been wanting some input ?

March 21, 2017 at 12:25 pm

If a painter uses the Divine Proportion and represents a human figure with a height of 2.6 feet, which of the following would measure 1 foot in length?

March 21, 2017 at 8:05 pm

The most common answer would be the distance from the navel to the top of the head. The ratio of 1.0 to 2.618 is the same as 0.382 to 1.0, so it defines the golden ratio of the height.

September 4, 2017 at 5:39 am

very informative it certainly proves that every thing is in accord in balance , yet surviving in a element of discord. I have done my own research on the symmetric aspects of the human body and have found the golden Ratio to be very accurate. further to your findings , I have discovered additional a /symmetrical/mathematical measurements of the human body, The length of the human face is equal to the length of the human hand. The circumference of the calf muscle is equal to the circumference of the neck. The distance from the centre of the sternum to the elbow is exactly half the distance as from the centre of the sternum to the FINGERTIPS. The length of the nose is exactly 1/3 the length of the face. The distance from the tip of the nose to the chin is equal to the length of the nose. The distance from the top of the nose to the hairline is equal to the length of the nose. (the golden ratio ) In the male within the human species; The distance from the human coxyn to the top of the shoulders. is 3 times the length of the foot ( as from the heal to the top of the ball of the foot ) The width of the person’s shoulders. 4.7 times the with of the ball of the foot.. The width of a persons hips is 4.7 times the width of the heal. So it can be concluded that the width of the foot is in direct proportion to the width of the human torso.

February 7, 2018 at 8:41 pm

This is all so interesting!

September 5, 2019 at 6:32 pm

This is all very interesting.. I am a violinist and have seen that the proportions on the making of a violin have almost on every corner the Golden ratio.. But at the beginning some VIOLINMAKER had to sit down and design this masterpiece. The sound inside travels also from this construction so that the best quality and quantity of sound can be produced. With all this knowledge and precision and patience a beautiful instrument is created and not evolved from matter.. It takes a humble step to see the magnificent MAKER behind the human body and the whole of creation even to the ends of the universe. This Mastermind that we Christians call God is greater and more intelligent than any of us and yet people assume this all came about by itself. In the beginning was the Word.. From dead matter to the high complex information that is needed to make even one protein in our body’s system, Is for me as a normal intelligent person, shear impossible… With all these thoughts think of the small instrument maker, the next time you go to a beautiful concert and maybe you will finally realize, while listening to the concert, the Great Maker who is behind the whole of creation.

October 13, 2020 at 10:30 pm

may i ask, does everyone havae a golden ratio? Because we have a assessment to measure some parts of our body which have golden ratio but I when I divide those values I can’t even get phi value ?

October 19, 2020 at 12:15 pm

Not everyone will have golden ratios in their proportions, but most people will have some proportions that are very close. The key thing is to know where to look for them. See these articles for guidance:

https://www.goldennumber.net/meisner-beauty-guide-golden-ratio-facial-analysis/ https://www.goldennumber.net/facial-beauty-golden-ratio-photo-analysis/ https://www.goldennumber.net/human-body/

October 23, 2020 at 7:55 am

Thank you so much.

January 26, 2021 at 7:21 pm

ever wonder why the very best(eg athletes,etc) and the healthy have close symmetry between left and right mirroring? contemplate

left and right, hands and feet.

bipedalism, momentum, ambidextrous-footness.

big knuckles connected to your….big foot knuckles. knees connected to your….elbows. break that down for each joint and connect them all together.

another example:

fingertips connected to your….toe tips, wrists connected to your….ankles.

your head, neck, ex/internal cavities. contemplate and read below.

you are what you do, and your body always remembers, TENSION.

now those measurements make sense? performance nothing to do with a balance of each segments, between left and right? how we perform our daily tasks? metabolism?

visible difference between 6 pack abs and 10 pack abs? never seen a tri athlete with 6?

man and woman Made for each other?

maybe more than we like to confront and Know.

January 26, 2021 at 7:28 pm

almost forgot to add, animals and nature. everything is connected, Everything. Tension

January 26, 2021 at 7:31 pm

almost forgot to add, animals and nature. everything is connected, Everything. TENSION

add to above 20/20 vision breathing 5 senses and their accompanying organs TENSION

May 24, 2021 at 8:38 am

I don’t even know why i’m here i’m gotta do golden ratio for math class but its the last week of school so i’m boutta say screw it

May 24, 2021 at 11:10 am

Well to make the golden ratio more interesting, pick a topic you like and see how it might apply: Sports, beauty, history, nature, DNA, etc. Type any one of those into the Search bar at the top right of https://www.goldennumber.net .

And to see how other people apply it, try my software site page at https://www.phimatrix.com/applications/. Download the two week free trial and apply it to some photos – people’s faces, famous artwork, etc.

For an overview to get you started, see:

https://www.goldennumber.net/golden-ratio/

A few interesting videos:

https://youtu.be/kKWV-uU_SoI https://youtu.be/nXDmAtTJ6JY

But if you just want the math try start here:

https://www.goldennumber.net/math/ https://www.goldennumber.net/geometry/

That should get you started, with a better head start than most everyone else in your class.

As Nike says, “Just Do It!”

August 29, 2021 at 9:29 am

the equation for PHI at the end of this article in wrong. correctly,

PHI= .5 (.5 + .5 + ( 5 ^ .5 ))

or PHI = (1/2) x ( 1 + sqrt5 )

September 4, 2021 at 9:57 am

The formula in article is correct, and quite simple. Copy and paste =5^.5*.5+.5 into Excel and it will produce 1.618034…

Your formulas are mathematically correct, but lack the simplicity and elegance of =5^.5*.5+.5

September 9, 2021 at 10:33 am

Sir! You are quite correct! but to be clear only ( .5 x ( 5 ^ .5 ) ) + .5 = PHI.

Thanks for setting me straight. One big attraction of my first formula is that it uses five 5s

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Design and the golden ratio

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The Golden Ratio in Photography: What it is, and How to Use it.

by Kelly @ Photography Hero | Composition in Photography , Most Popular

This here is next level stuff.

Rule of thirds. leading lines. All important, but they don’t capture the eye like the golden ratio.

If you’re ready to move past just placing your subject on a thirds line and calling it composition, read on. If not, don’t even think about reading more.

I say this in jest, as I hope you know, but the fact of the matter is that this compositional rule can be difficult to grasp and even harder to add into your images. However, if you can, the quality and appeal of your images will grow exponentially.

To start, understand that the golden ratio is applied to your images in many different ways and is known by many different names.  Some of the names you might be familiar with are: the golden mean, phi, Fibonacci spiral, or the divine proportion.  You may be familiar with one or more of these terms, but don’t be confused.

Each of these uses the golden ratio in a different way to create art, images and architecture that is pleasing to the human eye.

What is the Golden Ratio in Photography?

The golden ratio is a ratio of approximately 1.618 to 1. Artists have used this ratio for centuries to create works of art from paintings to architecture. Beethoven uses it in his famous fifth Symphony. It truly is all around us, including in our own bodies.

To see and understand the golden ratio, let’s take a line and divide it into two sections. If we follow the golden ratio, it would look like the image below, where A is the long side (1.618) and B is the shorter side (1).

The easiest place to see this on the human body is with the arm, although there are many other parts of the human body that follow the golden ratio.

For artists, the power of the golden ratio begins as this ratio is applied to other shapes. Let’s first construct what is called a golden rectangle. We do this, by taking the long side of the line that we labeled A, and matching that length to form the shorter sides of the rectangle.

This shape is used often in both modern and ancient architecture, the most famous being the Parthenon.

Read more about the golden ratio in architecture here .

Some have called the rule of thirds an oversimplified version of the golden ratio, and if you think about it, you can see why. By adding another vertical line to the golden rectangle, you will have a very close facsimile of the rule of thirds.

Fibonacci Sequence

In 1200AD, a mathematician named, Leonardo Fibonacci, discovered what is now known as the Fibonacci sequence which helped take the golden ratio even further. He took the numbers 0 and 1 and added them together to get 1.

He then continued taking the two previous answers and added them together to form this chain of numbers you see below.

The beauty of this chain of numbers is found when you take any two of the sums next to each other and divide the larger by the smaller. When you do this, you get a number very close to the golden ratio.  Look below.

5+18=13 and 8+13=21 are right next to each other in the Fibonacci sequence.  Take both of their sums, 13 and 21 and divide the largest by the smallest and you get an number very close to 1.618.

Do this with any of the sums in the Fibonacci sequence and you find the same thing.

Stay with me now, because we are not going to delve any more into math, so don’t quit reading on me!

Looking back to the golden rectangle, as I begin to add smaller golden rectangles inside the larger ones, something surprising happens.

The area of each of the newly formed squares is a sum of an equation in the Fibonacci sequence, and from this, we get the Fibonacci spiral which is what many artists use today as their main compositional technique.

Fibonacci Spiral

The spiral is created by drawing circular arcs from opposite corners of each square. Look at figure below to see the spiral inside the golden rectangle. This spiral is prolific in nature, most notably in the shell of the Nautilus.

Take notice, and you will see the golden ratio and Fibonacci spiral everywhere from the products you buy, to companies logos, to architecture.

It is well known by marketers who understand by following the golden ratio, people are more likely to view their products as favorable. We can use this to our advantage in our images as well.

Using The Golden Ratio in Photography

Below is the diagram that details the Fibonacci spiral with the main 1:1.618 lines. The Fibonacci spiral is one of the main ways photographers can use the golden ratio in photography.

Many famous photographers are known for their use of the golden ratio in photography. Ansel Adams used it often in his the landscape portraits that he captured.

© Ansel Adams

Henri Cartier-Bresson , one of my favorite photographers, used it as he capture life as it happened. Cartier-Bresson used a 50mm lens his entire career, focusing less on gear and more on composition. Below is a self-portrait he took using the Fibonacci spiral as the compositional technique.

Henri Cartier- Bresson

Look at these images and try to see the beauty in them. These are images of everyday life, but captured in a way that is interesting and though-provoking.  He had a powerful way of using the golden ratio in photography to bring the mundane to life.

Images above, © Henri Cartier-Bresson

In my mind, this is what photography is all about. Not about how much equipment we can buy or which lens is the largest. It’s about telling a story that is happening right before our eyes.

“To me, photography is the simultaneous recognition, in a fraction of a second, of the significance of an event.” -Henri Cartier-Bresson

Create using the Fibonacci spiral in Photography

The Fibonacci spiral is harder to grasp than say, balance or the rule of thirds. Those compositional rules are just easier to understand and put into use.

This is the reason many photographers have never heard of the Fibonacci spiral or the golden ratio in photography. It take more practice and focus to incorporate into your photographs. Let me share some ways you can begin incorporating the Fibonacci spiral into your image to help the composition of your images.

An easy way to begin to use the Fibonacci spiral is to shoot scenes of nonmoving objects and place them so they form a flowing number nine, with your subject at the circle of the nine. The image to the right is a good example of this.

Another way to create with the Fibonacci spiral is to use open space, or space that is of a different brightness than your subject.

On this image below, the eye is led to the subject by the shadowed person in the bottom left corner and the shadowed person on the right side. The light tones of the sky help bring the viewer into the image and then push the eye towards the subject.

This image of the surfers is another example.

Using the surfer at the bottom to lead the eye through the image, the viewer ends up at the surfer on the wave. You may be saying to yourself, “that’s just the rule of thirds.” You’re correct, the rule of thirds is a part of this image.

However, the surfer in the bottom left corner doesn’t follow the rule of thirds, yet adds balance, depth, and helps to lead the eye to the subject. That surfer in the bottom left brings all of this because he is placed in a location to use the Fibonacci spiral. Take a look at the images below.

Which do you prefer?

These subtle differences can take your images from good to great.

Create using the Golden Ratio in Photography

Creating images by thinking of a ratio can be can be incredibly difficult. To make things worse, each rectangle can be made into smaller golden rectangles as well. Take a look at the images below.  This is a mess of lines!

To complicate things further, golden ratio lines can also be diagonal. The image below shows how diagonal lines can make up the golden ratio, and again inside each set of lines, additional lines that follow the golden ratio can be added.  Into infinity.

To help solve some of this confusion, let me give some simple tips as you begin to use the golden ratio in photography.

TIP ONE: PLACE YOUR SUBJECT AT THE INTERSECTION OF LINES

As with the rule of thirds, placing your subject on an intersection of lines will help create a more pleasing image for the viewer. By doing this, it will cause you to leave in, or cut out something from the image you many not have done otherwise. The very act of doing this, will help shake up how you shoot images.

TIP TWO: PLACE STRONG LINES ON THE GOLDEN RATIO LINES

This tip is useful especially when photographing architecture with strong lines. Place those strong lines on the golden ratio lines to help create more interest in the image.

On the image of the building, the line between the dark and light portions of the building is placed on a golden ratio line, as well as the top corners.

In the bridge photo, the lines of the railing match golden ratio lines to help create an image that leads the viewers eye, and adds interest.

Annie Liebovitz

Have you ever seen group photo’s from Annie Liebovitz ?  She is far from the rule of thirds.  Most of group photo’s use the golden ratio.

© Annie Liebovitz

It can be confusing as you begin to incorporate the golden ratio into your images, because there are just so dang many ways!  I would suggest taking one or two methods and work on those before introducing others.

By doing this, you will become accustomed to using this technique, and as you get used to one or two methods, begin adding others.

Moving past the rule of thirds and using more advanced compositional techniques will truly help you to become a photographer with images that stand out.

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21 Comments

It seems to me that you can overlay the Golden Ratio on just about any image that includes several elements in it and the ratio seems to apply. Even Cartier-Bresson’s images as shown here don’t always fit the ratio perfectly and require a little imagination to accept that they do. Thoughts? PS: I teach Photojournalism and many of my students also ask this question.

I agree that the Golden Ratio can be tricky and even subjective. However, I think what is to be gained by attempting to create with the Golden Ratio, and all compositional rules, is to work to train our eye to see elements around our subject that can strengthen and reinforce it in the image. Obviously, every compositional rule can be stretched, warped and even broken, but the rules are there to help us see what others may not see to create a more powerful image. And, to help us get out of the default-to-the-rule-of-thirds notion with every image. Wouldn’t you agree?

I agree with you. I’m a mathematician and I have seen a lot of images with the Golden spiral overlaid just because someone said it is possible. I like memes about it.

When did perfection became a norm in art and photography? I think that imperfect photographs which are not following golden lines and Fibonaccy spiral are worth something as well.. It’s the emotion and story that a picture tells and life is rarely perfect. So why should photographs be?

Hey, could you tell me when was the article published? I can’t see it anywhere, I need it for a project in order to do bibliography. I want to use this article because is the best one, the more detail i find about Golden Ratio in Photography, so congratulations. But in order to do the biliography perfect I need the date or year of publishment!

I agree, but it probably depends on what kind of photograph it is. If it’s artistic expression, more freedom can be used. However, if it’s product photography and such, it’s probably good to consider what appeals most to people.

Every Artist is a Perfectionist. Photographers are no exception to that attitude. To my opinion, the article is very relevant and nicely presented. We always try to achieve perfection, but always it does not satisfy us, because we are not perfect. But, that does not/should not stop us to achieve perfection and that’s the drive for betterment every time we shoot.

You have made useful explanations and I thank you very much.|

Could you explain the lines in the Leibovitz group photo please?

Eva, my answer would be that she is using inverted triangles. Look at the head placement and notice the inverted triangles as you look from one head to the next. Her methods or mindset? Can’t help you there.

This was lovely, helped me understand it better than most other articles I read so far 🙂 Thanks!

Thanks so much!

Agree. A good article. Learn the mechanics, then intuition takes over after LOTS of practice.

This job was much more difficult than I thought. But I managed to learn more with the examples here. You explained it really well. It has been a very important resource for me.

So glad to hear!

CommentIt was a very important subject for me, your article has been a very important resource for me, thank you for this article.

You are so welcome!

this was an excellent article, thank you so much for explaining this complicated idea in the best way possible.

Glad to help!

Thanks for this great explanation! I’ll be keeping what you’ve shared here in mind the next time I go out shooting.

Hmm as some others have already said, whether it be golden spiral, golden triangle, golden whatever, sometimes it seems people are looking at someone’s well-composed photos and overlaying golden X on it and saying “He/she must’ve used this!” when the photographer probably just liked the way the shot looked while composing it. Many of the golden spiral images fits the 3rds rule better or golden triangle better or vice versa. In the end these are just vague guides at best and I seldom crop and line things up in post with the golden whatever grids. Good photography comes with experience and intuition on what makes a good composition, not deliberately lining things up.

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