a historical geometric journey with gsp assessing students understanding
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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

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

overview of presentation
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
pythagorean theorem
Pythagorean Theorem
  • Bhaskara’s Proof
  • Garfield’s Proof
  • Euclid’s Proof
  • Using Similar Shapes (instead of Squares) on the Sides of the Right Triangle
constructions using the theorem
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.
pythagorean triples
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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