Viviani’s Theorem from the Law of Conservation of Energy

<p>Recently I started reading the wonderful book, &ldquo;The Mathematical Mechanic&rdquo; by Mark Levi, in which he has proved a wide range of mathematical theorems using purely physical arguments.</p> <p>Inspired by some of these theorems, I decided to prove Viviani&rsquo;s theorem from a physics perspective. But first of all, what is Viviani&rsquo;s theorem?</p> <h1>Viviani&rsquo;s Theorem</h1> <p>Viviani&rsquo;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:</p> <p><a href="https://www.cantorsparadise.com/vivianis-theorem-from-the-law-of-conservation-of-energy-341c7b0ac5ad"><strong>Website</strong></a></p>