PYTHAGOREAN MATHEMATICS WITH TECHNOLOGY GSP AND A DIGITAL CAMERA

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PYTHAGOREAN MATHEMATICS WITH TECHNOLOGY (GSP AND
A DIGITAL CAMERA)
Armando M. Martinez-Cruz CSU Fullerton Amartinez-c
ruz_at_fullerton.edu
Paul Sexton Buena Park High School psexton_at_fjuhsd
.k12.ca.us
Greg Love Buena Park High School glove_at_fjuhsd.k12
.ca.us

• TASELM, CSU-FULLERTON
• Presented at
• NCTM - Atlanta
• March. 23, 2007

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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

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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.

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Pythagoras andTheorem of Pythagoras

• Bhaskaras Proof
• Garfields Proof
• Euclids 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 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.

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Conclusions and Questions