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