Viviani by Vectors

Here is a proof of Viviani's Theorem by Hans Samelson (Mathematics Magazine, Vol. 76, No. 3 (Jun., 2003), p. 225) that admits a generalization to equiangular polygons.

The sum of the distances from a point P in an equilateral to the three sides of the triangle is independent of the position of P (and so equal to the altitude of the triangle.)

A PWW of Viviani's theorem by Hans Samelson


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