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Exploring Pythagorean Mathematics with Technology: A Dynamic Approach using GSP and Digital Tools

This presentation delves into the integration of Pythagorean Mathematics with technology using Geometer's Sketchpad (GSP) and digital cameras. We highlight the importance of the Pythagorean Theorem and demonstrate various constructions including the Golden Rectangle, Quadrature of the Rectangle, and polygons like pentagons, hexagons, and decagons. The effectiveness of GSP as a pedagogical tool is discussed, emphasizing its user-friendly interface and capabilities. Join us for insights, demonstrations, and engaging discussions on mathematical investigations enhanced by technology.

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Exploring Pythagorean Mathematics with Technology: A Dynamic Approach using GSP and Digital Tools

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  1. PYTHAGOREAN MATHEMATICS WITH TECHNOLOGY (GSP AND A DIGITAL CAMERA) Armando M. Martinez-Cruz CSU Fullerton Amartinez-cruz@fullerton.edu Paul Sexton Buena Park High School psexton@fjuhsd.k12.ca.us Greg Love Buena Park High School glove@fjuhsd.k12.ca.us TASEL–M, CSU-FULLERTON Presented at NCTM - Atlanta March. 23, 2007

  2. Outline of Presentation • Welcome and Introduction • GSP Comments • Pythagoras and Theorem of Pythagoras • Constructions using the theorem: • Golden Rectangle • Quadrature of the Rectangle • Regular Pentagon • Pentagon, Hexagon and a Decagon • Pasting a digital picture into GSP • Conclusions and Questions

  3. Some Comments: • Software is extremely friendly, powerful and self-contained, but not perfect. • The power of the software lies on the ability to preserve the properties of Euclidean constructions when figures are dragged. • Strong tool for pedagogical purposes. • Constructions can be copied and pasted in other program documents but they become static. • Photos can be pasted in GSP docs. • Mathematical investigations are enticed. • Also good for analytic geometry.

  4. 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

  5. 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.

  6. Conclusions and Questions

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