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Measurement of a Circle

Archimedes

T. L. Heath, The Works of Archimedes (Cambridge, 1897)

A short treatise by Archimedes of Syracuse, probably part of a longer work now lost, presenting three propositions about the circle. The first proves that a circle's area equals that of a right triangle whose legs are the radius and the circumference; the third gives the celebrated bounds 3 10/71 < pi < 3 1/7 by comparing the perimeters of inscribed and circumscribed 96-sided polygons. It is among the earliest rigorous results on pi and a landmark of the Greek method of exhaustion.

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Contents

1. Proposition 1
2. Proposition 2
3. Proposition 3