Archimedes' Approximation of Pi - Maple Help

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Archimedes' Approximation of Pi

Main Concept

By increasing the number of sides in the polygon, the polygon's shape and area will approach that of a circle.

Explanation

The area of the n-sided polygon will be n times the area of one of its triangles.

Areapolygon 

=

nAreatriangle

where:

b is the base

h is the height

 

Areapolygon 

=

 n bh2

Areapolygon

=

12hnb

By rearranging the equation nb represents the perimeter of the polygon. As n increases the perimeter of the polygon approaches the circumference of a circle.

 

12r2πr

 

=

πr2

Adjust slider to change the number of sides that the polygon has.

 

Number of sides:

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