Viviani's Theorem III (visual proof without words via area) 

This is a short, animated visual proof of Viviani's theorem, which states that the sum of the distances from any interior point to the sides of an equilateral triangle is equal to the length of the triangle's altitude.
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This animation is based on a proof given on Alexander Bogomolny's website, cut-the-knot (www.cut-the-kn... ).
Here's are two alternative proofs using rotations or shifts and reflections:
• Viviani's Theorem (vis...
• Viviani's Theorem II (...
Here is a cool interactive GeoGebra applet to play with this theorem yourself:
www.geogebra.o....
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Music in this video:
Cinematic Experience by Alex-Productions | onsound.eu/
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