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Exploring Pythagoras: Theorem, Constructions, and Dynamic Software

Learn about Pythagoras, his theorem, and various constructions using dynamic software and a digital camera. Discover proofs by Bhaskara, Garfield, and Euclid, as well as unique geometric constructions like the Golden Rectangle and more. Presented by Paul Sexton from Buena Park High School and Armando M. Martinez-Cruz from CSU Fullerton at OCMC in Orange, CA.

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Exploring Pythagoras: Theorem, Constructions, and Dynamic Software

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

  3. 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

  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

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