Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (2024)

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

  • What Is the Golden Ratio?
  • 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
  • Summary
  • Want to Learn More?
  • Thanks for Reading!

(Bonus:Click here to download a PDF copy of my Color Theory Cheat Sheet.)

What Is the Golden Ratio?

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.”

What Is the Golden Ratio?

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 theParthenonstatues that seem to embody the golden ratio.
  • Euclid(c. 325-c. 265 BC), in hisElements, gave the first recorded definition of the golden ratio, which he called, as translated into English “extreme and mean ratio”.
  • Fibonacci(1170-1250) mentioned thenumerical seriesnow named after him in hisLiber Abaci. We will discuss the Fibonacci sequence later in this post.
  • Luca Pacioli(1445-1517) defines the golden ratio as the “divine proportion” in hisDivina Proportione.
  • Charles Bonnet(1720-1793) points out that in the spiralphyllotaxisof plants goingclockwiseand counter-clockwise were frequently two successive Fibonacci series.
  • Martin Ohm(1792-1872) is believed to be the first to use the termgoldener 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.

Calculations

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:

Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (1)

That weird symbol at the end represents the golden ratio.

I find this equation easier to understand in pictural format:

Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (2)

So a+b is to a asais tob.

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

The Golden Rectangle

Below is agolden 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.

Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (3)

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.

Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (4)

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.

Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (5)

Step 4 – Complete the golden rectangle.

Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (6)

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

The Fibonacci Sequence

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:

Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (7)

Golden Spiral

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

Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (8)

This spiral can be found throughout nature:

Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (9)

Applying the Golden Ratio in Art

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:

Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (10)

The Golden Section

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

Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (11)

The ratio of the columns is1: 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.

Examples of the Golden Ratio

My Website

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.

Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (12)

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.

Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (13)

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.

Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (14)

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

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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.

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

Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (17)

Summary

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.

Want to Learn More?

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

Thanks for Reading!

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!

Dan Scott

Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (18)

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Using The Golden Ratio (AKA Golden Mean) To Improve Your Artworks (2024)

FAQs

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

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

How do you use the golden ratio in art? ›

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

What is meant by the golden mean ratio in art? ›

The golden ratio is found when a line is divided into two parts such that the whole length of the line divided by the long part of the line is also equal to the long part of the line divided by the short part of the line.

What is the golden mean ratio quizlet? ›

Fibonacci numbers, like many elements found in nature, follow a 1:1.61 ratio - this is what we refer to as the Golden Ratio, and as it forms such a common sight in nature, it feels pleasing to the eye when we use this same ratio in our design work.

Why is the golden ratio important to art and design? ›

But when it comes to art, artists use this golden ratio because it is aesthetically pleasing. The golden ratio can be used in art and design to achieve beauty, balance, and harmony. Artists use the golden ratio as it helps in designing our paintings and is used to position the subjects.

Why is the golden ratio important? ›

The golden ratio has been used to analyze the proportions of natural objects and artificial systems such as financial markets, in some cases based on dubious fits to data. The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other parts of vegetation.

What is the principle of golden mean? ›

Moral behavior is the mean between two extremes - at one end is excess, at the other deficiency. Find a moderate position between those two extremes, and you will be acting morally.

What are the golden rules of painting? ›

And now, the golden rules.

It states that the elements of an artwork should be placed so that each element is in a proportion of 1 to 1.618 (around 3 to 5) in relation to any other element. The rule of thirds is a simplified version of the golden mean.

What is the golden ratio answer? ›

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.

What is the difference between golden mean and golden ratio? ›

The golden ratio, also known as the golden mean, the golden section or the divine proportion, is symbolized as the Greek letter phi. In mathematical terms, the golden ratio is an irrational number: 1.61803398874989484820...

What is the value of golden ratio in ratio? ›

Key Takeaways. The golden ratio is an irrational number that is equal to (1+√5)/2, or approximately 1.618...

Why does the golden ratio make things beautiful? ›

Others think that we tend to perceive a face more aesthetically appealing when it features the Golden Ratio because the human eye can process it faster and that causes our brain to feel 'pleased'. The Golden Ratio is not just observed in humans, but it is actually used in architecture and art work as well.

What is an example of the golden mean in real life? ›

For example, the measurement from the navel to the floor and the top of the head to the navel is the golden ratio. Animal bodies exhibit similar tendencies, including dolphins (the eye, fins and tail all fall at Golden Sections), starfish, sand dollars, sea urchins, ants, and honey bees.

What is unique about the golden ratio? ›

Now the clever part is that if you add the length of the long part 0.618… to the original length 1, you get 1.618… aka the Golden Ratio. It pops up everywhere in nature from sunflower petals to the spiral of a shell. It is even credited with the correct facial proportions that make people attractive.

How do you find the golden ratio of a face from a picture? ›

THE GOLDEN RATIO OF A BEAUTIFUL FACE
  1. the distance from the top of the nose to the centre of the lips should be 1.618 times the distance from the centre of the lips to the chin.
  2. the hairline to the upper eyelid should be 1.618 times the length of the top of the upper eyebrow to the lower eyelid.
May 23, 2017

What is the best ratio to take pictures? ›

For regular photos, then 3:2 or 4:3 would suffice. When choosing a format, think about the type of camera you have. To maintain quality, the ratio of your image size should never exceed your camera sensor's. For instance, if you're using a micro four-thirds camera, stick to 4:3 or 1:1.

What is the golden mean in simple terms? ›

: the medium between extremes : moderation.

What does gold mean in paintings? ›

In contemporary culture, gold continues to convey a myriad of different meanings, and is typically still used to symbolise prosperity, fortune and success.

What makes something golden? ›

If you describe something as golden, you mean it is wonderful because it is likely to be successful and rewarding, or because it is the best of its kind.

What is the Golden Mean in design? ›

The Golden Mean or Golden Proportion as it used to be called during the Renaissance is a way of guiding your composition towards a more pleasing visual effect. Using the Golden Mean as a strict rule in every design can end up dampening your creativity because you won't be thinking “out of the box”.

Where is the Golden Rule painting? ›

The work—originally presented to the UN in 1985 as a gift on behalf of the United States by then First Lady Nancy Reagan—was restored by Williamstown Art Conservation Center, which over the years has repaired numerous objects from Norman Rockwell Museum's collection as well (including Rockwell's 1953 United Nations ...

What does the 7 principles of art mean? ›

PRINCIPLES OF ART: Balance, emphasis, movement, proportion, rhythm, unity, and variety; the means an artist uses to organize elements within a work of art.

What are the three rules of art? ›

In composition, there are three rules or techniques we follow: the Rule of Thirds, Iconic and Leading the Eye.

What is the conclusion of the golden ratio? ›

Conclusion. Mathematically golden ratio is an irrational number, which means we can never achieve it perfectly in design; a debate going on forever.

What is golden ratio example numbers? ›

Golden Ratio Formula
New valueDivide by new valueAdd 1
1.51/1.5 = 0.666...0.666+1 = 1.666...
1.666...1/1.666... = 0.60.6+1 = 1.6
1.61/1.6 = 0.6250.625+1 = 1.625
1.6251/1.625 = 0.6153...0.6153+1 = 1.6153...
2 more rows
Oct 25, 2021

Where is the golden ratio found? ›

The “golden ratio” is a 1.618:1 mathematical ratio, and the number 1.618 is known as “phi.” Golden ratios can be found in shells, plants, flowers, and animals, among other places. It is believed to be one of the strongest and oldest connections between math and creative arts.

What is the golden ratio in art and music? ›

Mozart arranged his piano sonatas so that the number of bars in the development and recapitulation divided by the number of bars in the exposition would equal approximately 1.618, the Golden Ratio.

Why is the golden ratio aesthetically pleasing? ›

The reason we love the golden ratio, he argues, is that it's easy to grasp: According to Adrian Bejan, professor of mechanical engineering at Duke University, in Durham, North Carolina, the human eye is capable of interpreting an image featuring the golden ratio faster than any other....

What is the golden ratio of a canvas? ›

Using the golden ratio from the height of your canvas, make a line dividing the height of your canvas into a 1 to 1.618 ratio. Repeat, making 2 lines equally distant from the top and bottom of the canvas. All 4 lines should intersect. Consider placing the focal point of your composition near one of these intersections.

What artists were known for using the golden ratio? ›

During the Renaissance, painter and draftsman Leonardo Da Vinci used the proportions set forth by the Golden Ratio to construct his masterpieces. Sandro Botticelli, Michaelangelo, Georges Seurat, and others appear to have employed this technique in their artwork.

What is the golden ratio rhythm? ›

Music and poetry

The golden ratio is thus found in the 2/1 and 3/2 ratios, present in the two-beat, three-beat and four-beat rhythms. The ratio 5/3 is found in the five-beat measures.

What is an example of the golden ratio? ›

Examples of the Golden Ratio

Take honeybees, for example. If you divide the female bees by the male bees in any given hive, you will get a number around 1.618. 4 Sunflowers, which have opposing spirals of seeds, have a 1.618 ratio between the diameters of each rotation.

What makes the golden ratio perfect? ›

The Golden Ratio, also referred to as the Divine Proportion, states that when a line is divided into two parts in a ratio of 1: 1.618, it creates the ideal proportion.

What is the Golden Ratio for painting dimensions? ›

If you want a perfect Golden Ratio layout, set the dimensions to 1:1.618.

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