The Golden Section

A point divides a line segment in the golden section iff the proportion between the line segment and the longest part is equal to the proportion between the longest part and the shortest part, so

We will show how to construct a Pentagon (a regular 5-sided polygon) by means of the golden section.
First, we will prove that in a pentagon the proportion between a diagonal and a side is equal to the golden section.

Proof:
 
 

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Second, we will show how to construct a golden rectangle i.e. a rectangle where the proportion between the longest and the shortest side is equal to the golden section.

We need the following remark:

Given a square with side length 2:
 

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Finally, we use the above construction to construct a pentagon with a given side length. It's up to you to explain and to validate the construction.
 


Webpage by: Preben M Henriksen