Is it possible to place a lune on the hypotenuse of a right triangle whose area is equal to the sum of the areas of the other two lunes placed on the legs of the triangle? In this article, I use dynamic geometry software and spreadsheets in an attempt to answer this question along with the conditions satisfying the existence of such a lune. This in the classroom article also offers a method of investigating a trigonometric equation involving two variables using spreadsheets and dynamic geometry snapshots that are presented in a manner that complements the analytic and the visual approaches. I conclude by reinforcing the idea that the Pythagorean Theorem is indeed a relationship of areas, with or without the restriction that the lunes placed on the sides of a right triangle be similar.

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