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The Golden Ratio

Presentation outlining the Golden Ratio.

Jeff Grocott

on 16 October 2018

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Transcript of The Golden Ratio

The Golden Ratio
Look at these four rectangles and choose the one which you find most appealing?
Since the early Greeks, a ratio of length to width of approximately 1.618, has been considered the most visually appealing. This ratio, called the golden ratio, not only appears in art and architecture, but also in natural structures.
The Golden Rectangle is a unique and a very important shape in mathematics. The Golden Rectangle appears in nature, music, and is also often used in art and architecture. The special property of the Golden Rectangle is that the ratio of its length to the width equals to approximately 1.618:
Do these faces seem attractive to you? Many people seem to think so. But why? Is there something specific in each of their faces that attracts us to them, or is our attraction governed by one of Nature's rules? Does this have anything to do with the Golden Ratio?

Leonardo Da Vinci explored the human body involving the ratios of the lengths of various body parts. He called this ratio the "divine proportion" and featured it in many of his paintings including his most famous?
Another example of the golden ratio in architecture occurs in Egyptian pyramids. Ancient Egyptians used the Golden Ratio to build their pyramids about 2000 years before the Greeks built The Parthenon. In fact, the pyramids show one of the first examples of using the golden ratio in architecture.
If you said Rectangle C then you would agree with many artists and architects from the past. Rectangle C is called a Golden Rectangle and is said to be one of the most visually appealing geometric shapes. The ratio of length to width in a Golden Rectangle is the ratio
1 : 1.61803398
Phi is simply the ratio of the line segments that result when a line is divided in one very special and unique way. Divide a line so that:

Sectioning a line to form the golden section or golden ratio based on phi

the ratio of the length of the entire line (A)
to the length of larger line segment (B)

is the same as

the ratio of the length of the larger line segment (B)
to the length of the smaller line segment (C).
This happens only at the point where:

A is 1.618 … times B and B is 1.618 … times C.

Alternatively, C is 0.618… of B and B is 0.618… of A.
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