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A Historical Geometric Journey with GSP: Assessing Students’ Understanding

A Historical Geometric Journey with GSP: Assessing Students’ Understanding. Armando M. Martinez-Cruz, CSU Fullerton amartinez-cruz@fullerton.edu David Booze Troy High School dbooze1@earthlink.net Fernando Rodriguez Buena Park High School frodriguez@fjuhsd.k12.ca.us

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A Historical Geometric Journey with GSP: Assessing Students’ Understanding

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  1. A Historical Geometric Journey with GSP: Assessing Students’ Understanding Armando M. Martinez-Cruz, CSU Fullerton amartinez-cruz@fullerton.edu David Booze Troy High School dbooze1@earthlink.net Fernando Rodriguez Buena Park High School frodriguez@fjuhsd.k12.ca.us Presented at NCTM 2006 St. Louis, MO April 28, 2006

  2. Overview of Presentation • Welcome and Introduction, Class Project, GSP? • Fernando: Pythagoras, Bhaskara, Garfield, Euclid and Similar Shapes. • Armando: Some Applications of Pythagoras--Quadrature of Rectangle, Golden Rectangle, Pentagon, Hexagon, Decagon • David: An Extension: Pythagorean Triples • Conclusions and Questions

  3. Intro to GSP?

  4. Pythagorean Theorem • 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 that 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. Pythagorean Triples • A Visual Demonstration of the Relationship Between Pythagorean Triples and Pythagorean Quadruples • A Geometric Approach to Finding Pythagorean Triples • An Algebraic Approach to Finding Pythagorean Triples and Beyond

  7. Conclusions and Questions

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