Pi: The Never-Ending Number

When you start playing with geometry, you eventually come across the concept of pi. When you divide the circumference of a circle (the measurement of its perimeter) by its diameter (the width across its middle), you always get the same number. That number is pi. Whether you're measuring a large circle or a small circle, the circumference divided by the diameter always equals pi. Once you know the value of pi, you can easily figure out a circle's circumference, diameter, or area. It's a very useful number in geometry.

The approximate value of pi is 3.14159, if you round it off to make it easier to use in equations. In reality, pi is an infinite number. You can't accurately express it as a fraction (like 1/3 or 5/10) and it never repeats (like 3.333333 or 2.148148148). No matter how long or how hard you look, you'll never find a pattern in the numbers. Mathematicians have calculated pi to billions of decimal places, but still have not found any pattern or repetition to the numbers.

Pi has a long history. The earliest mention of the idea was in an Egyptian papyrus dating to more than 3,500 years ago. The Egyptians understood that the ratio of a circle's circumference to its diameter was constant. They expressed pi using fractions, and figured it as (4/3)⁴ (about 3.16). The Babylonians had it figured as 3 + 1/8 (about 3.125).

The ancient Greeks also understood pi as a ratio between a circle's circumference and diameter. By experimenting with circles inside polygons, Archimedes, a Greek mathematician who lived in about 200 B.C., proved that pi was somewhere between 3 10/71 and 3 1/7 (or about 3.14, roughly what we know it to be today).

At last count, pi has been calculated to more than 50 billion decimal places. The power of modern computing has made calculating pi as much a competitive pastime as a serious calculation. Here is a piece of pi (forgive the pun). The number below is pi calculated to the 1,000th decimal place:

3.141592653589793238462643383279502884
19716939937510582097494459230781640628
62089986280348253421170679821480865132
82306647093844609550582231725359408128
48111745028410270193852110555964462294
89549303819644288109756659334461284756
48233786783165271201909145648566923460
34861045432664821339360726024914127372
45870066063155881748815209209628292540
91715364367892590360011330530548820466
52138414695194151160943305727036575959
19530921861173819326117931051185480744
62379962749567351885752724891227938183
01194912983367336244065664308602139494
63952247371907021798609437027705392171
76293176752384674818467669405132000568
12714526356082778577134275778960917363
71787214684409012249534301465495853710
50792279689258923542019956112129021960
86403441815981362977477130996051870721
13499999983729780499510597317328160963
18595024459455346908302642522308253344
68503526193118817101000313783875288658
75332083814206171776691473035982534904
28755468731159562863882353787593751957
78185778053217122680661300192787661119
59092164201989