Harmonic proportions

A trapezium with its diagonals and a parallel line segment. Prove that yellow : purple = blue : red.

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Solution by Kamran Zamani.


Harmonic proportions
Or golden ratio
An excellent number
For harmony
Honored by Pythagoras
A tool for applications
Written by Fibonacci
For the so called most beautiful number
The golden ratio describes beauty
Some say, the number theory is the queen of mathematics


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