### Examples of the Golden Ratio – architecture and nature [Adam Tan]

Phi in Architecture

The UN Tower

The west face of the UN Secretariat consists of three main window panels. It may not seem so close up, but when viewed from afar, it is evident that each panel is the Golden Rectangle.

This design was formed by Le Corbusier using his ‘Modulor’ system in 1943 and presented to the US in 1946, a year prior to the construction of the UN Secretariat.

The Pyramids of Giza

Currently the oldest monument with the use of phi in its architecture, the Pyramids of Giza incorporate the golden ratio correct to the fifth decimal place. The ratio of the slant of the pyramid to the distance from ground centre is 1.61804… The name given to such triangles is the Egyptian Triangle.

Toronto’s CN Tower

Phi can be found in the CN Tower in nothing more than its height. The full height of the tower (553.33m) to the height of the observation deck (342m) gives the golden ratio.

Phi in Nature

Bodies

Though it may not seem like it, the proportions of several areas of the body bring the result of phi. The ratio of the height of your entire body to the height of your naval to your head is, in fact, the golden ratio. Even animals reveal the golden ratio; each section of an ant in relation to another brings out phi.

Reproductive dynamics

Within a honey bee colony, when the number of females is divided by the number of males, the quotient is often very close to 1.618. Additionally, the family tree of any given bee will represent the Fibonacci sequence (which, of course, has a close relationship with the golden ratio). Males have one, female, parent, and females have both male and female parents. And so, when bees are asked to draw out their family trees, the number of bees they would receive would be 2, 3, 5, 8, 11 etc. respectively.

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