Golden Ratio or the Divine Proportion

Ever wondered why certain things in nature, certain human faces, and bodies or some popular architectural buildings are so aesthetically pleasing to eyes?

Turns out that they have one thing in common, the Golden Ratio. The Golden Ratio denoted by greek letter phi φ is also called the Divine Proportion or the golden mean.

So what exactly is this Golden Ratio (φ)?

Imagine if there is a perfect number, a single number so flawless that it formed the basis for all art and music. A number so important that it could be used across the disciplines of mathematics & physics and a number so profoundly purposeful that the natural world and the universe would bend to its whims.

That number is 1.6180, so let’s find out why it is so important?

If you have studied mathematics until your senior secondary school, you are probably familiar with Fibonacci Sequence which forms the basis of the golden ratio.

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, …

In the Fibonacci sequence, any two consecutive numbers can be added to find the next in the sequence. This string of digits is of fundamental importance and today we apply this knowledge in all manners of practical ways. Search algorithms, stock trading, gambling odds, all make use of the Fibonacci sequence, but the way in which you have most likely encountered it is via the mysterious Golden ratio (φ).

The golden ratio is the limit of the ratios of successive terms of the Fibonacci sequence.

The Golden Ratio

In other words, if a Fibonacci number is divided by its immediate predecessor in the sequence, the quotient approximates φ; e.g., 987/610  1.6180327868852. These approximations are alternately lower and higher than φ and converge to φ as the Fibonacci numbers increase.

Mathematical Definition of Golden Ratio

If you have a number a  and a lower number then the two are in Golden Ratio if the ratio between the sum of a b v/s a  is similar to the ratio between a v/s b :

The Golden Ratio

The Golden ratio is a special number found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part. It is often symbolized using phi, after the 21st letter of the Greek alphabet.

Golden Ratio

The greek letter ascribed to this ratio is φ and its value is contracted to 1.6180. Basically anything which comes close to this value in terms of its ratio is said to be perfectly proportioned. For example, a rectangle that measures 12.94 cm x 8 cm is in the Golden Ratio.

The use of φ in Art & Architecture

The Phi( φ ) or the Divine Proportion has been one of the fundamental basis of design, architecture, art & music. It has fascinated the world’s most knowledgable people ever since its discovery and its influence can be seen in some of the finest works mankind has ever produced.

Plato’s study into the Golden Ratio was used in the designs of the Parthenon, the former temple on the Athenian Acropolis, Greece, dedicated to the goddess Athena.

The Egyptians displayed it in the planning and construction of the pyramids.

Egyptian Pyramid Golden Ratio

The Taj Mahal was also built according to this important mathematical law.

Michelangelo’s The Creation of Adam on the ceiling of the Sistine Chapel also utilizes the golden ratio rule.

Da Vinci’s Mona Lisa also incorporates the principles of the Golden ratio or the divine proportions.

The idea of using the Golden Ratio in design is to produce the work that is aesthetically pleasing by creating a sense of beauty through harmony and proportion.

Get a line art caricature of yourself or your loved one’s drawn & adorn the walls of your home with a framed piece of art.

The use of φ in Web & Graphic Design

The modern-day artists and designers & architects know about the golden ration and are known to apply it purposefully to their works.

Twitter Logo Golden Ratio

The famous twitter logo was designed with the circles in the golden ratio.

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The Pepsi logo was designed with circles in the Golden Ratio.

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  • National Geographic’s famous golden rectangle icon logo is in Golden Ratio and symbolizes the very nature of our universe which follows this universal aesthetical law in everything.
  • The Apple logo, as well as the Apple iCloud logo, also follows the divine proportions.

  • The car manufacturers often use the principles of divine proportions to build aesthetically pleasing cars.

Human beauty is based on the Golden Ratio or the Divine Proportion Phi ( φ).

The human face is packed with examples of the Phi( φ ), also known as the Golden Section or Divine Proportion. It has long been said that beauty is in the eye of the beholder. This phrase can be rephrased in scientific and mathematical terms as :

“Beauty is in the phi of the beholder.”
Is human facial beauty related to the Golden Ratio? How many Golden Ratios are there in a beautiful face? This video features Florence Colgate, voted Britain’s “Most beautiful face” for 2012 and searches for the presence of Golden Ratios in her facial features and proportions using PhiMatrix golden ratio design and analysis software.

The scientific evidence, suggests that our perception of physical beauty is hard-wired into our brains and is based on how closely the features of one’s face reflect phi(φ) in their proportions.

Reference to Golden Ratio in movie Super 30
In this still, from movie Super 30, actor Hrithik Roshan who played the role of mathematician Anand Kumar can be seen making reference to the Phi( φ ) of the face of his love interest played by actress Mrunal Thakur

Creating Shapes in Golden Ratio

Now after learning all about the Phi( φ ) and its application in art, architecture, and design, you might be wondering how to create the shapes that are in the golden ratio. In this section, we will cover the basics step by step. So let’s get started.

Step No. 1: Create a square of dimension 50px X 50px.
Step No. 2: Create another square adjacent to it of the same dimension i.e.; 50px X 50px.
Step No. 3: Create a square below these two of double dimension i.e.; 100px X 100px.
Step No. 4: Now Draw another square of 150px X 150px dimension on the left of these squares.
Step No. 5: Now on top of this draw another square of 250px X 250px dimension.
Step No. 6: Now on the right side of this draw another circle of 400px X 400px dimension.

You have now got a grid for the shapes in the golden ratio. You can now draw circles in each of these squares and use them in your logo constructions while making sure that you do not change the ratio of their proportions with each other.

You can as well create golden spiral by joining the diagonals of each of these squares with an arch.

Golden Ratio Spiral

If you made it this far in this post congratulation 🙂 You now have the understanding of this magical number in mathematics. If you liked this post consider giving a like by clicking the like button below and sharing this on your social media.

Further Reading

If you are further interested in learning how to use the principles of the golden ratio or the divine proportion in your work head over to following links one by one.
How to use Phi( φ ) in your design layout
How to use Phi( φ ) in your spacing
How to use Phi( φ ) in your content
How to use Phi( φ ) with your images

Categories: Design


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