1. Pythagoras Meets Dynamic Software and a Digital Camera Summary Presented at OCMC – Orange, CA March. 10, 2007 Armando M. Martinez-Cruz CSU Fullerton Amartinez-cruz@fullerton.edu Paul Sexton Buena Park High School psexton@fjuhsd.k12.ca.us

2. Outline of Presentation Welcome and Introduction GSP Comments Pythagoras and Theorem of Pythagoras Constructions using the theorem: –Golden Rectangle –Quadrature of the Rectangle –Regular Pentagon –Pentagon, Hexagon and a Decagon Conclusions and Questions

3. Pythagoras and Theorem of Pythagoras Bhaskara’s Proof Garfield’s Proof Euclid’s Proof Using Similar Shapes (instead of Squares) on the Sides of the Right Triangle

4. Constructions using the Theorem Golden Rectangle A Square with the Same Area of a Given Rectangle, aka, Quadrature of Rectangle Pentagon, hexagon and decagon inscribed in the same circle. Actually, it is possible to construct a triangle with one side of the pentagon, one side of the hexagon, and one side of the decagon. And that triangle happens to be a right triangle.

5. Conclusions and Questions