Archimedes' Approximation of Pi - Maple Programming Help

Home : Support : Online Help : Math Apps : Algebra and Geometry : Geometry : MathApps/ArchimedesApproximationOfPi

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.

$=$

$n\cdot \left({\mathrm{Area}}_{\mathrm{triangle}}\right)$

 where: b is the base h is the height

$=$

${\mathrm{Area}}_{\mathrm{polygon}}$

$=$

$\frac{1}{2}\cdot h\cdot \left(n\cdot b\right)$

By rearranging the equation $n\cdot b$ represents the perimeter of the polygon. As n increases the perimeter of the polygon approaches the circumference of a circle.

$\frac{1}{2}\cdot r\cdot \left(2\cdot {\mathrm{π}}_{}\cdot r\right)$

=

${\mathrm{π}}_{}\cdot {r}^{2}$

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

 Number of sides:

 More MathApps