Transcript THEOREM OF PYHTAGORAS AND GSP FOR GOLDEN …

THEOREM OF PYHTAGORAS AND
GSP FOR GOLDEN RECTANGLE,
REGULAR PENTAGON AND
QUADRATURE
Armando
Martinez-Cruz
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CSU Fullerton
[email protected]
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Paul Sexton
Buena Park High School
[email protected]
Presented at
CMC-Palm Springs
Nov. 4, 2006
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Outline of Presentation
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• Welcome and Introduction
• Pythagoras and Theorem of Pythagoras
• Constructions using the theorem:
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Golden Rectangle
Regular Pentagon
Pentagon, Hexagon and a Decagon
Quadrature of the Rectangle
• Conclusions and Questions
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Pythagoras and
Theorem of Pythagoras
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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
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• 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.
• Some extensions of the Theorem
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Conclusions and Questions
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