The orange fraction

A square containing a quarter circle and a red equilateral triangle. What’s the orange fraction?

Scroll down for a solution to this problem.


The orange fraction is 1/4.

Solution by Dmitriy Spiridonov.


The orange diamond
Shines brightly
Jewel in the crown
Precious and rare
It is the envy of many
A big almond
For billions of dollars
The orange sapphire
Looks like a fire opal
A very rare and
Pure stone
And without any defect
The orange diamond
Is perfect


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One reply on “The orange fraction”

Easy it easy enough to check that when the orange wedge has angle 30 degrees, the other triangle is isosceles. But, derivations I’ve seen using algebra or trigonometry to solve for the angle 30 do not seem very satisfying.

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