Here’s an interesting formula:
Arctan(1) + Arctan(2) + Arctan(3) = Pi.
(Everything’s in radians, of course).
Presentation Suggestions:
Challenge students to prove this fact.
The Math Behind the Fact:
The Figure contains a hint; check that the angles of the three triangles at their common vertex add to Pi. Can you find a similar proof for the following equation?
Arctan(1/2)+Arctan(1/3) = Pi/4.
How to Cite this Page:
Su, Francis E., et al. “One, Two, Three, Pi.” Math Fun Facts. <https://www.math.hmc.edu/funfacts>.
References:
R. Nelsen, Proofs without Words. p.39.
R. Vakil, A Mathematical Mosaic, 1996. p.86.
Fun Fact suggested by:
Stan Wagon