Viviani’s Theorem from the Law of Conservation of Energy
<p>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.</p>
<p>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?</p>
<h1>Viviani’s Theorem</h1>
<p>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:</p>
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