PYTHAGOREAN MATHEMATICS WITH TECHNOLOGY (GSP AND A DIGITAL CAMERA) TASEL–M, CSU-FULLERTON Presented at NCTM - Atlanta March. 23, 2007 Armando M. Martinez-Cruz CSU Fullerton Paul Sexton Buena Park High School Greg Love Buena Park High School

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 –Pasting a digital picture into GSP Conclusions and Questions

Some Comments: Software is extremely friendly, powerful and self-contained, but not perfect. The power of the software lies on the ability to preserve the properties of Euclidean constructions when figures are dragged. Strong tool for pedagogical purposes. Constructions can be copied and pasted in other program documents but they become static. Photos can be pasted in GSP docs. Mathematical investigations are enticed. Also good for analytic geometry.

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

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.

Conclusions and Questions