• Ar. Stephanie L.P. Chan


by Anees Aafiqah

The Golden Ratio is known to have the Fibonacci Sequence related to it. Calculating the ratio of successive pairs as you go higher in the Fibonacci sequence gives a closer value to the Golden Ratio. The Golden Ratio can be found everywhere, in nature and in man-made features; be it in buildings, paintings or even food. The Golden Ratio has been called in different names; Golden Mean or Golden Section, Extreme and Mean Ratio, Medial Section, Divine Proportion, Divine Section, Golden Proportion, Golden Cut and Golden Number.


Same as the number Pi(π), The Golden Ratio, also known as Phi(Φ), is an irrational number which has the value of 1.618033...etc. It is when two parts of a straight line divided into two, (a): longer section and (b): shorter section, where the ratio of (a) to (b) is equals to the ratio of (a)+(b) to (a).

Image: Golden Ratio received from



Golden ratio is a common mathematical ratio found in nature which can be used in artworks and project designs. Golden Ratio is used in art and design to make beautiful shapes and to find aesthetically pleasing proportions. The Golden Ratio has been used by artists throughout the history. During the Renaissance, Leonardo Da Vinci, along with other artists, have used the Golden Ratio in their artworks.

Image: Mona Lisa Golden Ratio received from



The Golden Ratio or Section has been used for centuries in geometrical constructions to determine aesthetically pleasing proportions and divisions; it provides a sense of balance and equilibrium which is pleasing to the eye. Architects have been taking advantage of The Golden Mean in their designs to bring balance and height, to give varying shapes, and as per mentioned, to make the buildings more aesthetically pleasing.

Architects have been using the Golden Rectangle to find balance to a structure. The golden rectangle signifies any shape that can be divided into a square and rectangle which have lengths and widths which corresponds to the ratio which implies that the ratio can still be maintained if the resulting rectangle is continuously divided again into smaller segments. This helps Architects to precisely adjust the proportion of their design to make it bigger or smaller.

In addition, architects have not just used the golden triangle, they have also used the golden triangle and logarithmic spiral that allow them to create variety of shapes for their design. A Golden triangle is a triangle in which the ratio of smaller side with its adjacent side is the golden ratio. A Logarithmic Spiral can be created by bisecting the angles of a golden triangle to make another one and is done continuously.

Image: Logarithmic Spiral with Golden Triangle received from


A famous example of the presence of Divine Proportion is in Ancient Greek Architecture of The Parthenon. The Greeks were aware of the aesthetics effects in architecture with the use of Golden Ratio and thus using it in their designs.

Image: Parthenon Divine Proportion received from



The Golden Ratio can be expressed throughout the human body in numerous ways, including our bodies’ formation and functioning.

To cite an example; In 2009, there was a study showing that the Golden Ratio may be an important predictor of heart attacks published in the British Medical Journal.

In this study, Professor Hanno Ulmer and his team have analysed the blood pressure readings of significant number of subjects and found that the ratio between systolic and diastolic of those who were less likely to get a heart attack is 1.6180 which is the Golden Ratio.


Baker, Stephen Lanzalotta, has applied the golden ratio on diets which helps him to uncover the diet plan for weight loss and good health and named it the Diet Code. The Diet Code incorporates a balance of healthy food in the best combinations and appropriate amount for one’s diet. He used the Golden Ratio to form his diet plant of 52% carbohydrates, 20% protein and 28% fat.

On a different note, exterior and interior designs of constructions which are based off of the Golden Ratio and Fibonacci Sequence may improve the wellbeing and mental health of an individuals. As mentioned in this article, the Golden Ratio have been used by architects and designers to make their designs more appealing and pleasing to the eye. Fractals, inspired by the golden ratio, have been used in their designs and a study have found that viewing patterns like fractals have been helpful in reducing stress.

Below are some examples of fractal used in designs

Image: Federation Square, Melbourne retrieved from


Image: Fractal Design retrieved from


Image: Indoor Fractal Forest retrieved from


In short, The Golden Ratio is a mathematical phenomenon that is applicable in various aspects. It varies from analysing the perfect proportions in arts and design to the functionality of the human body. It has also been used to help improve the wellbeing and mental health of an individual by facilitating in the reduction of stress through the increase in the aesthetic appeal in designs and architecture.

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