Exploring Archimedes’ Practical Approach to Calculating pi in a Technology Based Teacher Education Program

Virtual Showcase ID: 33613
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    Mohammad Yazdani
    University of West Georgia

Abstract: We define pi as the ratio of the circumference of a circle to its diameter. We also define a circle as a regular polygon with infinite sides. Employing this concept man has been trying to calculate the value of pi for centuries. Babylonians calculated pi = 25/8 (the distance that a wheel with the diameter of 8 unit travels in one complete revolution), Egyptians founded pi = 256/81 (the area of a circle with the radius of nine units is the same as the area of a square with sides of 16 units). However Archimedes used the perimeters of polygons inscribed and circumscribed about a given circle to calculate the circumference of the circle. He calculated the perimeters of inscribed and circumscribed 6, 12, 24, 48, and 96 sided regular polygons. The perimeters of inscribed and circumscribed 96-gons were calculated to be very close to each other. He used that perimeter as the circumference of the circle. He calculated3.1408<pi<3.1429. In this project we employed CBRI II Geometry software to examine Archimedes’ strategy.

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