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Approximating Pi Using Inscribed and Circumscribed Circles of Regular Polygons

​
number of sides
3
incircle area
π
4
circumcircle area
π
polygon area
3
3
4
inner error
3
3
4
-
π
4
outer error
π-
3
3
4
error ratio
3.58725
From the inscribed and circumscribed circles of a regular polygon we determine the area of each, along with the corresponding errors. As you add more sides, the error for the circumscribed circle approaches twice that of the inscribed circle.

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