The book of science

Tom Sharp

Johann Heinrich Lambert, Ferdinand von Lindemann mathematics



Squaring the circle

To “square the circle” is to find the length of the sides of a square with the same area as a circle of a given radius. The area of a circle of radius r is πr2 , so success depends on the nature of π. The proofs of Lambert and Lindemann mean that we know that it is impossible for anyone to construct on a flat surface a square with the same area as a given circle using a compass and ruler.

The expression “squaring the circle” means trying to do the impossible.

Archimedes used the “method of exhaustion” to approximate the value of π. The work of both Archimedes and Liu Hui prefigured calculus; Archimedes wrote of infinitesimals and Liu Hui described the use of the limit.

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