Recently I started reading the wonderful book, “The Mathematical Mechanic” by Mark Levi, in which he has proved a wide range of mathematical theorems using purely physical arguments.
Inspired by some of these theorems, I decided to prove Viviani’s theorem from a physics perspective. But first of all, what is Viviani’s theorem?
Viviani’s Theorem
Viviani’s theorem states that the sum of the distances from any point in the interior of an equilateral triangle to each of the sides is a constant. No matter where you are in the triangle, this sum will be the same. A particular configuration is given in the diagram below: