A ubiquitous and strange number
Pi is defined formally as the ratio of the circumference (C) of a circle to twice the radius (r). This was known in antiquity even before mathematicians tackled this ratio. As such, it is an amazing discovery, which tells us that no matter the size of a circle, the ratio of the circumference to the diameter (twice the radius) never changes. This might strike us as obvious, but the obvious often holds many hidden treasures. Like the Pythagorean theorem, π established something that people knew practically and mathematicians gave this knowledge an abstract form, so that it could be used and studied further. And it has produced incredible results. This chapter deals with π, and its appearances in other part of mathematics and in Nature, reminding us that it is there, and defying us to understand why. The more technologically advanced we become and as our picture of π grows ever more sophisticated, the more its mysteries grow.
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