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.
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Pythagorean Theorem with Hippocrates’ Lunes,
Spreadsheets in Education (eJSiE):
2, Article 5.
Available at: http://epublications.bond.edu.au/ejsie/vol8/iss2/5