Five Pi Formulas in "Pi/2 minutes" (Pi Day visual proofs)
In this short video, we give five different formulas for pi (or related constants) using only a single diagram consisting of a 2x3 rectangle and a triangle inside. Using the fact that the tangent of an angle is the ratio of the opposite and adjacent sides of an angle (and you can get the angle using the arctangent of the appropriate ratio), we decompose angles (of measure pi/4, pi/2, and pi) using certain triangles with visually computable arctangents using the diagram.
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This visual proof is due to Rex Wu and comes from the March 2003 issue of The College Mathematics Journal (https://www.jstor.org/stable/3595783 ) see pages 115 and 138.
For more Pi-related videos, check out my playlist:
• Pi
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