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The approach of Archimedes for approximating π

© T Madas Archimedes knew that the area of a circle was given by its radius squared, multiplied by a constant number ( π ) He also knew that the circumference of a circle was given by its radius doubled and further multiplied by the same constant number ( π ) He used regular polygons and by increasing the number of their sides, he found a good approximation for π

A regular polygon is inscribed inside the circle The circle is inscribed inside a regular polygon The area of the circle lies between the areas of these two regular polygons

20 sided regular polygon

30 sided regular polygon

Archimedes used regular polygons with up to 96 sides A table which simulates his findings looks as follows: He was able to use his findings to approximate π to good accuracy

Perimeter (4 d.p.) Area (4 d.p.) Number of sides of regular polygon All the regular polygons are inscribed in circles of unit radius This means that both their perimeter & area will get closer to π as their number of sides increases

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… 1000 d.p.

© T Madas … 5000 d.p.

© T Madas … d.p.

© T Madas … d.p.

© T Madas