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Circling the Square: Cwmbwrla, Coronavirus and Community

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In 1914, Indian mathematician Srinivasa Ramanujan gave another geometric construction for the same approximation. In modern mathematics the terms have diverged in meaning, with quadrature generally used when methods from calculus are allowed, while squaring the curve retains the idea of using only restricted geometric methods.

Ancient Indian mathematics, as recorded in the Shatapatha Brahmana and Shulba Sutras, used several different approximations to π {\displaystyle \pi } .The more general goal of carrying out all geometric constructions using only a compass and straightedge has often been attributed to Oenopides, but the evidence for this is circumstantial.

Contemporaneously with Antiphon, Bryson of Heraclea argued that, since larger and smaller circles both exist, there must be a circle of equal area; this principle can be seen as a form of the modern intermediate value theorem. Greek mathematicians found compass and straightedge constructions to convert any polygon into a square of equivalent area.

This identity immediately shows that π {\displaystyle \pi } is an irrational number, because a rational power of a transcendental number remains transcendental. After Lindemann's impossibility proof, the problem was considered to be settled by professional mathematicians, and its subsequent mathematical history is dominated by pseudomathematical attempts at circle-squaring constructions, largely by amateurs, and by the debunking of these efforts. In contrast, Eudemus argued that magnitudes cannot be divided up without limit, so the area of the circle would never be used up. Despite the proof that it is impossible, attempts to square the circle have been common in pseudomathematics (i. Having taken their lead from this problem, I believe, the ancients also sought the quadrature of the circle.

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