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