Wolfram Demonstrations Project

Let

stand for the areas of the regions colored red, blue, orange, and green, respectively.

In the right graphic, observe that

. Moreover,

, because:

and

Therefore the red area is

In the case

, the red area is

Reference: Füsun Akman, "Proofs without Words under the Magic Curve," The College Mathematics Journal, 33(1), 2002 pp. 42–46.

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