What is the history of mathematical pi?

Answer 1

The ancient Egyptians and Babylonians knew that there was a constant ratio between the circumference of a circle and its diameter. The Egyptians used the approximate value 3 and 1/8 (=3.125) around 2000 BC. This is always a constant which is evident from the equation:

2 x Pi x r = circumference.

The ancient Greek mathematician Archimedes (287-212 BC) proved that pi is between 3 and 1/7 and 3 and 10/71, in around 240 BC. In decimal notation this puts pi between 3.1408 and 3.1429, which is good enough for most practical purposes. In fact 3 and 1/7, or 22/7, is good enough for most purposes. Note that pi is not exactly equal to any ratio of whole numbers.

Note that pi is not exactly equal to 22/7, or to any ratio of whole numbers. See the answer below for quite a few digits. It is a constant irrational value. It's most accurate value is approximately

3.14159 26535 89793 23846 26433 83279 ...

(Note the three dots at the end means pi goes on for ever without repeating.)

The ratio of the circumference to the diameter of a circle is the same for all circles. This fact was known to ancient Egyptian, Babylonian, Indian and Greek mathematicians.. The earliest known approximations of Pi are from around 1900 BC; they are 25/8 (Babylonia) and 256/81 (Egypt), both within 1% of the true value.

The actual symbol, the Greek letter, was not used until 1706, but the concept is 4000 years old.

The first person that used pi would be the Greeks and the Archimedes from Syracuse. The mathematician figured out that pi = 3.14 or 3 1/7.

Pi is the ratio between the circumference and the diameter of a circle.

In the past, Pi has been calculated in a number of ways. One of the first mentions of pi can be found in The Bible. The first major breakthrough in the calculation of pi (before it was just approximations such a route 10) was by Archimedes. He calculated the circumference of a circle with radius 0.5 but circumscribing polygons around a circle, and increasing the number of sides on the polygon. He got to 96 sides.

Later, Leibniz learnt to calculate Pi (around the 16th century) through approximating Arctan1, which is Pi (in radians). There is an infinite series for Pi which was found by Taylor a few years earlier. The infinite series for pi was:

1 - 1/3 + 1/5 - 1/7 + 1/9... = Pi/4

This was followed by a number of other breakthroughs which lead to the computer age of calculating pi. With that, the calculation of Pi to several trillion decimal places was possible.

In modern times, pi has almost been made less accurate by government legislation. Many bills have been proposed in the United States over the years to make pi exactly equal to 3. The reasoning has ranged from "biblical accuracy" (quoting a ratio of three cubits to one cubit) to raising test scores. Many rumors about certain politicians trying to enact this legislation prove not to be true, but a few attempts have been made. Most of these attempts are quickly squelched early in the legislative process, but one 1897 attempt in Indiana made it all the way to the state senate before being killed.