What Is The Golden Ratio?

Everything about the Golden Ratio starts from mathematics, from what so-called “Fibonacci numbers” which generates a sequence like the following:

the golden ratio












This sequence represents an arithmetical path starts by 0 up to infinity( ∞ ), to be each number plus the one follows it (within the sequence) then dividing the result on the result of the preceding ones (within the sequence) is nearly (1.6) up to (1.61803398875) as to be Approximated to (1.618). That’s what called the Golden Ratio or the Perfect Ratio, & It’s symbolized by the symbol (φ).

Any two amounts achieve the golden ratio if the ratio of the sum of their two quantities to the largest amount between them is equal to the ratio of the largest to the smallest quantity. Have you found that hard to understand?

Look at the following figure:

Where did it come from?

The golden ratio has been a very high focus of attention for scholars and intellectuals since ancient times, from the Greeks Euclid and Pythagoras to the Italian mathematician Leonardo Fibonacci, as well as figures from modern history such as novelist Dan Brown in his novel “The Da Vinci Code.”

No one invents mathematics and its applications; it was there in nature since the beginning of the universe. Alike for the golden ratio, it exists in everything around us from the beginning and was discovered in very ancient times.

There are many arguments about its first discoverer. Some attributed it to the Pharaohs, because of what modern science has discovered about their applications to the golden ratio in their pyramids and sculptures of their kings. Herodotus referred to the proportionality of the Pyramid saying; “I was informed The Egyptian priests that the proportionalities in the Great Pyramid between the base side and the height allowed him to have the square created at the height equal to exactly the area of each of the triangular facets of the pyramid,” in addition to the fact that the king’s room in the Pyramid of Khufu, also, achieves the golden ratio.

Pyramid of Khufuthe Great Pyramid








But the most likely narrative is that the Greeks were the first to develop precise scientific theories and applications for the golden ratio. Such as Geomorphology or Geometry, which combines mathematics with design and arts. the first to use them was the mathematician Euclid, and the world still uses their sciences to this day.

Geomorphology in old roman Romans golden ratio






We can see the perfect application for the golden ratio, at the site where the Kaaba was built in Mecca, Saudi Arabia. It has been scientifically proven that its geographical location is determined in a manner identical to the golden ratio between the Earth’s south and the north pole.

Earth golden ratio

The Golden Ratio Applications:

The Golden Pyramid

It is the square base pyramid, that, its height line from its base is perpendicular to half the baseline at a 90°.

Golden Pyramid

The Golden Rectangle

It is a rectangle that each one of its sides achieves the golden ratio.

Golden Rectangle

The Golden Section

We can define it as the line that passes through all consecutive Fibonacci rectangles (without intersection) to infinity.

the Golden Section

The Golden Triangle

It is the triangle in which the length of the base side to the length of the other two shades is the golden ratio.

Golden Triangle

The Golden Ratio & Nature

If we look at the nature around us, we find everything tightly crafted according to the golden ratio. Starting with the human body, where the length of the foot to the pelvis relative to the length of the pelvis to the shoulder achieves it. & the length of the wrist to the elbow relative to the length from the elbow to the shoulder also achieves it. As well as, the size of the fingers of the hand & even the face. All of it achieves the golden ratio.

human body golden ratio

Golden Ratio in Animals & Plants

The golden ratio is achieved in animals (in different ways) for example in hives, science has shown that the number of females in any hive exceeds the number of males by a constant percentage and this percentage is (1,618/ the Golden Ratio) as another example, if we look at the bodies of the following animals we find that they achieve the golden ratio with high accuracy.

animals golden ratio animals golden ratio animals golden ratio




Even plants don’t grow randomly; they grow identically to the golden ratio, which is scientifically known as the golden growth, where plants first grow from a small group of individual cells known as structural tissue.

This tissue is found in the limbs of plants (twigs, leaves, & so on.) and produces new cells and as soon as the plants grow. What distinctive here, is that the main structural tissue (in the trunk) produces new cells in a spiral form called spirals where they turn at a specific angle once producing a new cell, and then the structural cells that it produces continue to do the same. This pattern of rotation follows the golden ratio where it results in perfect growth; if the rotation weren’t there, you would not see the shape of flowers as it looks like now. and this ratio is 0.618 and proved by the French mathematicians Yves Couder and Stephanie Dawadi in 1993.

planet flowers







Golden Ratio & Design

Most modern science areas have benefited from its applications, such as architecture, in which a building is hard without the use of it. To various industries such as automobiles, aircraft, and ships.

Nowadays, most international companies are using the golden ratio in each design for their UIs, logos & everything represents their visual identity.

Nike adidas apple golden ratio toyota





Applying the Golden Ratio in Modern Design

As we have seen before. Most large Corps adopt the use of the golden ratio in the design of their logos and visual identities. You can also benefit from it if you are a designer or painter in any field.

The ideal design of the UIs must provide users with a flexible & responsive experience. Sometimes, designers make a great effort in producing consistent work in terms of color tones and overall appearance. But when looking at the final UI, it seems unsatisfactory/visually uncomfortable.

Why? The reason for this is that it does not rely on the golden ratio in the design of its infrastructure.

By understanding the ideal design of the UI structure you’re working on, you’ll create excellent work. That can attract viewers and makes them feel comfortable. We can do this, by applying it to the measurements of each component of the UI. Where science has proven that we consider (unconsciously) anything follows it as ideal or perfect.

Designing the Ideal Smartphone Apps’ UI

You can use it to design the sizes and locations of the application or web page UI components for smartphones.

You can apply the golden rectangle to UI’s. This helps to determine the ratios of content sizes (e.g. bottom bar) to the ratio of the interface.

In the following example, we draw the golden rectangle vertically on the app UI; This allowed us to determine where to place the bottom options bar. As to make it, more suitable for the audience eye. And so, we just put all the components of the interface based on the golden ratio that formed this rectangle.

app UI

Designing the Ideal Web UI

You can also use it to design web UIs, like the following screenshot. You can achieve that, by applying the golden rectangle to the overall UI. Then to determine where to place the logo & how large it is. As well as, the ratio of the upper-bar size to the rest of the UI components. All defined by the visual hierarchy. The measurement of each component must be proportional (with golden ratio 1.618) to the previous larger one.

Web UI

Typography & The Goldin Ratio

People determine whether they like the content they come across from the very first moment their eyes fall on it. & inconsistent, content — with a very large title —, for example, may seem uncomfortable for them. Thus,  you should consider the ideal content design, before publishing any text.

When viewing texts on an interface, it seems self-evident that you should evaluate them hierarchically as the orators, subheadings & paragraphs. But that’s not everything. Designers can also apply the golden ratio for the sub-title size to the title in a hierarchical manner. Then the size of the paragraph that follows relative to the size of the title above it. You can achieve this through the following steps:

  1. Set the size of the larger title.
  2. Divide the title size by the gold ratio (1.618).
  3. The result of that division is the appropriate size for subheadings or for the next paragraphs, and so on.

For example, the size of the title in this article is (18). To know the ideal font size for the following paragraph, we divided (18/1.618). That showed us, that the optimal size for its font is (11). Then repeated the same pattern in paragraphs and titles followed.

Drawing the shape of the golden ratio (ideal rectangle):

The ideal design rectangle can be drawn using any design software, such as Adobe Illustrator and others, in the following way:












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