# Approximating Pi with Inscribed Polygons

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Increase the number of sides of the polygon to see it approximate the unit circle. As the number of sides increases, the area of the polygon approximates the area of a circle with increasing accuracy, showing that the value of π can be estimated with regular polygons.

Contributed by: Rob Morris (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

An *n*-sided regular polygon can be broken up into *n* equally-sized triangles; the area of the polygon is simply the area of one triangle multiplied by the number of triangles (*n)*. By increasing the number of sides of the regular polygon, it begins to approximate a circle. Thus, a good approximation to the area of a circle can be found by simply finding the area of a single triangle!

Archimedes originally used a similar method over 2200 years ago to calculate the value of π to two decimal places.

## Permanent Citation

"Approximating Pi with Inscribed Polygons"

http://demonstrations.wolfram.com/ApproximatingPiWithInscribedPolygons/

Wolfram Demonstrations Project

Published: March 7 2011