Trigonometry by Watching

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Trigonometry by Watching:

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Explanation

Hopefully, the demonstration above made it pretty obvious that the purpose of this page is to prove the trigonometric identity

$\arctan(1)+\arctan(2)+\arctan(3)=\pi.$

That identity has been established elsewhere from several viewpoints and also by paper folding.

The present demonstration (which is due to John Molokach) appears to be the most effortless. The demonstration is artfully using the properties of the famous 3-4-5 (Egyptian) triangle.

 

Trigonometry

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