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

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

Armando M. Martinez-Cruz,

CSU Fullerton

amartinez-cruz@fullerton.edu

David Booze

Troy High School

Fernando Rodriguez

Buena Park High School

frodriguez@fjuhsd.k12.ca.us

Presented at NCTM 2006

St. Louis, MO

April 28, 2006

• 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

• Garfield’s Proof

• Euclid’s Proof

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

• 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.

• 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