1. THEOREM OF PYHTAGORAS AND GSP FOR GOLDEN RECTANGLE, REGULAR PENTAGON AND QUADRATURE Presented at CMC-Palm Springs Nov. 4, 2006 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 Pythagoras and Theorem of Pythagoras Constructions using the theorem: –Golden Rectangle –Regular Pentagon –Pentagon, Hexagon and a Decagon –Quadrature of the Rectangle 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. Some extensions of the Theorem

5. Conclusions and Questions