The definition of pi and a brief history of pi?

Answer 1

Pi is the ratio between the diameter and the circumference of a circle. It is also coincidentally the ratio between the area and the radius squared for a circle. It is approximately 3.1415926535897932 and is irrational, meaning that it cannot be expressed as the fraction of two integers, and that its digits never terminate or repeat in a pattern. Also, it is transcendental, meaning that it is not algebraic, i.e. that it is not the root of any polynomial with rational coefficients.

Pi has been used for thousands of years, in the times of the Egyptians when they built their pyramids and by the Greeks, Babylonians, and Chinese.

Archimedes, who lived ~250 B.C.E., calculated that PI was between 3+10/71 and 3 10/70 (3+1/7 or 22/7). He was the first known person to have studied PI extensively. Ptolemy, a later scholar, gave PI as approximately 3.1416. Later, Liu Hiu of what would later become China also stated PI as 3.1416 around 265 AD. He then produced a very quick algorithm, and Zu Chongzhi, another Chinese mathematician, proved that 3.1415926 < PI < 3.1415927 in 480 AD. For this method, he used a 12288-gon.

Maimonides then states the irrationality of PI in the 12th century. Later developments in estimations were very limited for the next 1000 years, until in 1424, when Jamshid al-Kashi correctly estimated PI to 16 digits.

Today, we know pi to more than a trillion digits.