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## Important Facts About Pi

Pi is probably the most important mathematical constant. It appears in various formulas throughout mathematics and science in various fields such as physics, statistics and sociology. Although pi is defined in terms of the geometry of a circle, most applications of this number do not involve circles directly.

Since ancient times, people have been obsessed with pi. This is not a surprise, because the circle is one of the most basic, but at the same time interesting, geometric figures. Pi is defined as the ratio of the circumference to the diameter of the circle. (Any round will work, since all rounds are the same.) Rounded to 10 decimal places, the value is 3.1415926536.

Part of what makes pi interesting is that it appears in several other formulas that involve perimeters or areas. For example, the area of a circle is pi times the square of its radius. Also, the surface area is 4 pi times the square of its diameter, and its volume is 4/3 pi times its cube. In fact, the formulas for the contents of all higher dimensional analogs of the pi field are included.

As mentioned, pi also appears in many formulas that do not directly involve perimeters or areas. For example, the periods of all trigonometric functions are either pi or 2 pi. Although radius functions may be expressed in terms of a circle, they are often used in contexts that do not directly involve circles. Another place where pi is widely used is in the normal distribution, commonly used in statistics, whose formula is the square root of pi.

The calculation of pi has a long and interesting history. Some of the most elaborate mathematical methods have been used in creating various formulas for pi. At the end of the 19th century, its value was calculated by hand in several hundred tenths. Since the dawn of the computer era in the mid-20th century, the number of pi digits has grown exponentially. As of 2002, its value is known to over a trillion decimal places – enough to fill a large library!

Part of the reason some mathematicians are interested in computing the many numbers of pi is to look for patterns in its numbers. So far, no obvious ones have been found. It is assumed that pi is a normal number, meaning that any infinite number of digits in any base will occur infinitely many times in pi with the same frequency as would be expected if the digits were random.

In 1995, a surprising formula for pi was discovered, which allows one to calculate the hexadecimal (base 16) numbers of pi without having to calculate the previous numbers. This formula was used in 2000 to calculate the hexadecimal number (10^15th) of pi, which equals 0. Several similar formulas have since been discovered, some in other bases, but none in base 10 has yet been found.

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