Pi Times Phi using a Regular Icosagon Area (visual proof) @MathVisualProofs

Uploaded September 2024 | Updated September 2026, 2 weeks ago

In this video, we use a golden triangle to find the area of a regular icosagon sitting inside of the unit circle (the circle with radius 1). From this area formula, we are able to then find an interesting bound on the product of two famous constants: Pi and the golden ratio.

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If you like this video, you might enjoy this compilation of four visual proofs finding the area of a regular dodecagon inscribed in the unit circle: youtu.be/I5IrNug26S8

This animation is based on a visual proof by Roger B. Nelsen from a recent issue of The College Mathematics Journal (doi.org/10.1080/07468342.2024.2347160 ).

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Pi Times Phi using a Regular Icosagon Area (visual proof)

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