Problem
Trigonometry Without a Word
Two arctangent identities, seen through a geometric proof without words.
Prove the following two equalities
\[\begin{aligned} \arctan(\frac 12) + \arctan(\frac 13) = \frac \pi 4\\ \arctan(1) + \arctan(2) + \arctan(3) = \pi. \end{aligned}\]Explore the solution
A proof without words.