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THEOREM OF PYHTAGORAS AND GSP FOR GOLDEN RECTANGLE, REGULAR PENTAGON AND QUADRATURE

Explore Pythagoras' theorem through Bhaskara’s, Garfield’s, and Euclid’s proofs. Learn constructions with the theorem like Golden Rectangle and Regular Pentagon inscribed in circles. Discover quadrature of rectangle and various polygon constructs. Conclude with extensions and questions.

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THEOREM OF PYHTAGORAS AND GSP FOR GOLDEN RECTANGLE, REGULAR PENTAGON AND QUADRATURE

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  1. THEOREM OF PYHTAGORAS AND GSP FOR GOLDEN RECTANGLE, REGULAR PENTAGON AND QUADRATURE Paul Sexton Buena Park High School psexton@fjuhsd.k12.ca.us Armando M. Martinez-Cruz CSU Fullerton Amartinez-cruz@fullerton.edu Presented at CMC-Palm Springs Nov. 4, 2006

  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 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. • Some extensions of the Theorem

  5. Conclusions and Questions

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