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PYTHAGOREAN MATHEMATICS WITH TECHNOLOGY (GSP AND A DIGITAL CAMERA)

PYTHAGOREAN MATHEMATICS WITH TECHNOLOGY (GSP AND A DIGITAL CAMERA). Armando M. Martinez-Cruz CSU Fullerton Amartinez-cruz@fullerton.edu. Paul Sexton Buena Park High School psexton@fjuhsd.k12.ca.us. Greg Love Buena Park High School glove@fjuhsd.k12.ca.us. TASEL–M, CSU-FULLERTON

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PYTHAGOREAN MATHEMATICS WITH TECHNOLOGY (GSP AND A DIGITAL CAMERA)

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  1. PYTHAGOREAN MATHEMATICS WITH TECHNOLOGY (GSP AND A DIGITAL CAMERA) Armando M. Martinez-Cruz CSU Fullerton Amartinez-cruz@fullerton.edu Paul Sexton Buena Park High School psexton@fjuhsd.k12.ca.us Greg Love Buena Park High School glove@fjuhsd.k12.ca.us TASEL–M, CSU-FULLERTON Presented at NCTM - Atlanta March. 23, 2007

  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 • Pasting a digital picture into GSP • Conclusions and Questions

  3. 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.

  4. 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

  5. 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.

  6. Conclusions and Questions

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