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Archimedes’ Geometric Insights: Circle, Triangle, and Polygon

Explore the relationship between circle, triangle, and polygon areas based on Archimedes' principles in Paradise 33:130-145.

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Archimedes’ Geometric Insights: Circle, Triangle, and Polygon

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  1. Dante’s Geometer Math club, Feb. 13, 2008

  2. Paradise 33:130-145

  3. The measure of the circle … …is the measure of this triangle -- (Archimedes)

  4. The area of the polygon grows at each step, and approaches the area of the circle A0. If the triangle has less area than the circle, then eventually the polygon has larger area than the triangle.

  5. But the area of the polygon is LESS than (1/2)RC. Its “R” is less, and its “C” is less.

  6. Paradise 33:130-145

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