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From the Fun Fact files, here is a Fun Fact at the Medium level:

One, Two, Three, Pi

Figure 1
Figure 1

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. <>.

Keywords:    trigonometry, geometry
Subjects:    geometry
Level:    Medium
Fun Fact suggested by:   Stan Wagon
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