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Approximation of Pi using Inscribed Polygons - Archimedes

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Archimedes found his approximation to Pi by inscribed polygons.

Start with a circle of radius 1 and a suitable starting polygon and solve for an inscribed polygon of 96 sides.

Next, start with a unit circle and appropriate inscribed regular polygon to approximate Pi using a regular inscribed n-gon with 4096 sides.

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A step-by-step and clear solution to the approximation of pi using inscribed polygons is provided.

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First we note that the perimeter of an n-sided regular polygon inscribed in a circle of radius r is given by
P = 2 n r sin(π/n), and the ratio of perimeter to the diameter of the circle is: 2 n r sin(π/n) / 2r = n sin(π/n).
Let's ...

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