Webster's Collegiate Dictionary defines π as "1: the 16th letter of the Greek alphabet... 2 a: the symbol pi denoting the ratio of the circumference of a circle to its diameter b: the ratio itself: a transcendental number having a value to eight decimal places of 3.14159265"
A number can be placed into several categories based on its properties. Is it prime or composite? Is it imaginary or real? Is it transcendental or algebraic? These questions help define a number's behavior in different situations. In order to understand where π fits in to the world of mathematics, one must understand several of its properties: π is irrational and π is transcendental.
The History of π
In the long history of the number π, there have been many twists and turns, many inconsistencies that reflect the condition of the human race as a whole. Through each major period of world history and in each regional area, the state of intellectual thought, the state of mathematics, and hence the state of π, has been dictated by the same socio-economic and geographic forces as every other aspect of civilization. The following is a brief history, organized by period and region, of the development of our understanding of the number π.
In ancient times, π was discovered independently by the first civilizations to begin agriculture. Their new sedentary life style first freed up time for mathematical pondering, and the need for permanent shelter necessitated the development of basic engineering skills, which in many instances required a knowledge of the relationship between the square and the circle (usually satisfied by finding a reasonable approximation of π). Although there are no surviving records of individual mathematicians from this period, historians today know the values used by some ancient cultures. Here is a sampling of some cultures and the values that they used: Babylonians - 3 1/8, Egyptians - (16/9)^2, Chinese - 3, Hebrews - 3 (implied in the Bible, I...