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Archimedes' Approximation of Pi
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Main Concept
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By increasing the number of sides in the polygon, the polygon's shape and area will approach that of a circle.
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Explanation
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The area of the n-sided polygon will be n times the area of one of its triangles.
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![Area[polygon]](/support/helpjp/helpview.aspx?si=8330/file02225/math43.png)
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![n*Area[triangle]](/support/helpjp/helpview.aspx?si=8330/file02225/math49.png)
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where:
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b is the base
h is the height
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![Area[polygon]](/support/helpjp/helpview.aspx?si=8330/file02225/math81.png)
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![Area[polygon]](/support/helpjp/helpview.aspx?si=8330/file02225/math91.png)
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By rearranging the equation  represents the perimeter of the polygon. As n increases the perimeter of the polygon approaches the circumference of a circle.
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≈
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=
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Adjust slider to change the number of sides that the polygon has.
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number of sides:
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