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


Related material
Read more...

  • Equilateral and 3-4-5 Triangles
  • Rusty Compass Construction of Equilateral Triangle
  • Equilateral Triangle on Parallel Lines
  • Equilateral Triangle on Parallel Lines II
  • When a Triangle is Equilateral?
  • Viviani's Theorem
  • Viviani's Theorem (PWW)
  • Tony Foster's Proof of Viviani's Theorem
  • Viviani in Isosceles Triangle
  • Slanted Viviani
  • Slanted Viviani, PWW
  • Morley's Miracle
  • Triangle Classification
  • Napoleon's Theorem
  • Sum of Squares in Equilateral Triangle
  • A Property of Equiangular Polygons
  • Fixed Point in Isosceles and Equilateral Triangles
  • Parallels through the Vertices of Equilateral Triangle

    • |Contact| |Front page| |Contents| |Geometry|

    Copyright © 1996-2018 Alexander Bogomolny

    73920393