Pi, represented by the Greek letter π, is a mathematical constant approximately equal to 3.14159. It's the ratio of a circle's circumference to its diameter and appears in many mathematical and physics formulas.
*Key Properties:*
- *Irrationality*: Pi is an irrational number, meaning it can't be expressed exactly as a ratio of two integers.
- *Transcendence*: Pi is a transcendental number, making it impossible to solve the ancient challenge of squaring the circle with a compass and straightedge.
- *Random Digit Distribution*: Pi's decimal digits appear randomly distributed, but no proof of this conjecture has been found.
*Approximations:*
- *Integers*: 3
- *Fractions*: 22/7, 333/106, 355/113
- *Decimal Digits*: 3.14159 26535 89793 23846 26433...
*History:*
- Ancient civilizations, including Egyptians and Babylonians, approximated Pi for practical computations.
- Greek mathematician Archimedes developed a polygonal approach to approximate Pi around 250 BC.
- Mathematicians have attempted to extend their understanding of Pi for thousands of years ¹#NewsTrade