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A Historical Geometric Journey with GSP: Assessing Students’ Understanding PowerPoint PPT Presentation


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A Historical Geometric Journey with GSP: Assessing Students’ Understanding. Armando M. Martinez-Cruz, CSU Fullerton [email protected] David Booze Troy High School [email protected] Fernando Rodriguez Buena Park High School [email protected]

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A Historical Geometric Journey with GSP: Assessing Students’ Understanding

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A historical geometric journey with gsp assessing students understanding l.jpg

A Historical Geometric Journey with GSP: Assessing Students’ Understanding

Armando M. Martinez-Cruz,

CSU Fullerton

[email protected]

David Booze

Troy High School

[email protected]

Fernando Rodriguez

Buena Park High School

[email protected]

Presented at NCTM 2006

St. Louis, MO

April 28, 2006


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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


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Intro to GSP?


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Pythagorean Theorem

  • Bhaskara’s Proof

  • Garfield’s Proof

  • Euclid’s Proof

  • Using Similar Shapes (instead of Squares) on the Sides of the Right Triangle


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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.


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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


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Conclusions and Questions


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