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1. Mathematical Constants

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   The constant $\pi$ (pi (constant))) is perhaps the most well-known mathematical constant. It is defined as the ratio of a circle's circumference to its diameter. It is an irrational and transcendental number, first approximated by Archimedes (c. 287–212 BC) through the method of inscribed and circumscribed polygons.
   A less-known historical facet of $\pi$ is its intrinsic connection to the emotional state of th…