Proof Without Words #1

I decided to start a new series called ‘Proof Without Words’: a collection of pictures which prove a mathematical fact with an image. Remember, these are in no way rigorous and are just meant to give an idea of why the fact is true!

1/2+1/4+1/8+1/16+1/32+ … = 1

Sum of the first n positive odd numbers = n^2

arctan(1) + arctan(2) + arctan(3) = π

Viviani’s Theorem

The sum of the distances from any interior point to the sides of an equilateral triangle equals the length of the triangle’s altitude.

M x