Math 459, Senior Seminar
10/6/2011
Name: Alyssa Eubank
Title: The Pythagorean Theorem
Source: Darko Veljan, The 2500-Year-Old Pythagorean Theorem, Mathematics Magazine, 73
(Oct. 2000), no. 4, 259-272.
Senior Project Ideas:
1. Explore the relationships of the sides a right triangle in Euclidean and non-Euclidean
geometries in attempt to discover a more generic “Pythagorean Theorem” that
encompasses more than one geometric space. This project would deepen your
knowledge and understanding of non-Euclidean geometries.
2. Create an in-depth lesson where students would explore and discover the Pythagorean
Theorem. This could involve making visual aids in Geometer’s Sketchpad (GSP) or to
create a lesson that ask students to explore The Pythagorean Theorem on their own in
GSP.
3. Explore other interpretations of The Pythagorean Theorem (i.e. areas of Pythagorean
triple circles) and their applications. In this process, try and discover your own
interpretation and prove it rigorously. Also explore the many proofs of The Pythagorean
Theorem and attempt to discover a new proof. This project would deepen your
understanding of the rigor of The Pythagorean Theorem and would give experience
similar to that of mathematics research.