What is circumference over diameter? Today we refer to it simply as pi. This somewhat mysterious ratio interested people of all ages for centuries. This ratio is ancient and goes back to the beginning of civilization.

Although some historians believe that pi was discovered earlier, the first real traces of pi go as far back as the Bible itself. Of course, the value of pi back then was calculated by hand, using crude tools. As a result, pi was thought to equal 3. This might seem very rough to a modern person. In fact, the great temple of Solomon, around 950BC, used 3 as the value for pi. Surprisingly, the Egyptian Rhind Papyrus, around 1650 BC, shows a good evidence taht the value of pi was thought to be 4(8/9)^{2}, which is 3.16.

At the time around 200 BC, a great mathematician named Archimedes, of Syracuse, came along. He was also mystified by pi. However, unlike all the rest, Archimedes did not claim to have found the exact value of pi. He, on the other hand, obtained an approximate value of 223/71 < pi < 22/7. Archimedes derived that astonishing value without the advantages of algebraic or trigonometric notations, and he did not know of decimals. To calculate this value, he resorted to polygons, and went all the way up to 96-sided figures!

There were many more people involved in the process of determining pi. Most of them did not make any new theories, but merely used Archimedes' method and went to higher polygons. Below is a chart of most of these people:

Rhind Papyrus - 2000 BC - 1 decimal place correct

Archimedes - 250 BC - 3 decimal places correct

Vitruvius - 20 BC - 1 decimal place correct

Chang Hong - 130 - 1 decimal place correct

Ptolemy - 150 - 3 decimal places correct

Wang Fan - 250 - 1 decimal place correct

Liu Hui - 263 - 5 decimal places correct

Tsu Ch'ung Chi - 480 - 7 decimal places correct

Aryabhata - 499 - 4 decimal places correct

Brahmagupta - 640 - 1 decimal place correct

Al-Khwarizmi - 600 - 4 decimal places correct

Fibonacci - 1220 - 3 decimal places correct

Madhava - 1400 - 11 decimal places correct

Al-Kashi - 1430 - 14 decimal places correct

Otho - 1573 - 6 decimal places correct

Viète - 1593 - 9 decimal places correct

Romanus - 1593 - 15 decimal places correct

Van Ceulen - 1596 - 35 decimal places correct

Newton - 1665 - 16 decimal places correct

Sharp - 1699 - 71 decimal places correct

Seki Kowa - 1700 - 10 decimal places correct

Kamata - 1730 - 25 decimal places correct

Machin - 1706 - 100 decimal places correct

De Lagny - 1719 - 112 decimal places correct

Takebe - 1723 - 41 decimal places correct

Matsunaga - 1739 - 50 decimal places correct

von Vega - 1794 - 136 decimal places correct

Rutherford - 1824 - 152 decimal places correct

Dase Strassnitzky - 1844 - 200 decimal places correct

Clausen - 1847 - 248 decimal places correct

Lehmann - 1853 - 261 decimal places correct

Rutherford - 1853 - 440 decimal places correct

Shanks - 1874 - 527 decimal places correct

Ferguson - 1946 - 620 decimal places correct

In the year 1761, Lambert proved that pi was irrational. In other words, it could not be written as a ratio of integer values. In about a hundred years, in the year 1882, Lindeman proved that pi was also transcendental. That is, pi is not a root of any algebraic equation with rational coefficients. This proved that a circle does not have a square root, a question that has been troubling mathematicians for generations.

Listed below are the first 1001(including the 3) digits of Pi:

3.1415926535897932384626433832795028841971693993751

05820974944592307816406286208998628034825342117067982148

08651328230664709384460955058223172535940812848111745028

41027019385211055596446229489549303819644288109756659334

46128475648233786783165271201909145648566923460348610454

32664821339360726024914127372458700660631558817488152092

09628292540917153643678925903600113305305488204665213841

46951941511609433057270365759591953092186117381932611793

10511854807446237996274956735188575272489122793818301194

91298336733624406566430860213949463952247371907021798609

43702770539217176293176752384674818467669405132000568127

14526356082778577134275778960917363717872146844090122495

34301465495853710507922796892589235420199561121290219608

64034418159813629774771309960518707211349999998372978049

95105973173281609631859502445945534690830264252230825334

46850352619311881710100031378387528865875332083814206171

77669147303598253490428755468731159562863882353787593751

9577818577805321712268066130019278766111959092164201989

As you can see, the legacy of pi was a very long one. It took centuries to get the pi to what it is now. Luckily, with the invention of a computer, this task has been simplified down to a simple algorithm. Now, practically every calculator and every single computer can calculate pi. Below is a link to a website that allows you to see the 200 millionth decimal place of pi. Warning: this crashed my computer!

http://www.math.com/

http://www.hepl.phys.nagoya-u.ac.jp/~mitsuru/pi-e.html

http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Pi_through_the_ages.html