arXiv:2008.07995math.HO
How Archimedes showed that $π$ is approximately equal to 22/7
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Abstract
The ratio of the circumference, C, of a circle to its diameter, D, is a constant number denoted by $π$ and is independent of the size of the circle. It is known that $π$ is an irrational number and therefore cannot be expressed as a common fraction. Its value is approximately equal to 3.141592. Since Archimedes was one of the first persons to suggest a rational approximation of 22/7 for $π$, it is sometimes referred to as Archimedes' constant. In this article, we discuss how Archimedes came up with his formula. Archimedes in fact proved that 223/71 < $π$ < 22/7. Here we provide an improved lower bound.
https://en.wikipedia.org/wiki/Approximations_of_π The method of using inscribed and circumscribed n-gons conceptually is the simplest (1), but converges very slowly. See https://arxiv.org/pdf/2008.07995.pdf. (1) at least to non-mathematicians. Pure mathematicians will want to…
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