# pi

Pi is a numerical constant that represents the ratio of a circle's circumference to its diameter on a flat plane surface.The value is the same regardless of the size of the circle. The decimal expansion of pi is a nonterminating, nonrepeating sequence of digits. For most calculations, the value can be taken as 3.14159. This means, for example, that a circle with a diameter of 10 centimeters, as measured on a flat surface, has a circumference of approximately 31.4159 centimeters.

The number pi is also the ratio of the diameter of a sphere to the length of any great circle (geodesic) on the sphere.So, for example, if the earth is considered to be a perfect sphere with a diameter of 8,000 miles, then the distance around the earth, as measured along the equator or along any great circle, is approximately 8,000 x 3.14159, or 25,133 miles.

Pi is an irrational number.It cannot be precisely defined as the ratio of any two whole numbers.Thus, its decimal expansion has no pattern and never ends.The first few hundred, thousand, million, or billion digits of pi can be calculated using a computer to add up huge initial sequences of the terms of an infinite sum known as a *Fourier series*.Mathematically, it can be shown that the following equation holds:

The symbol to the left of the equal sign is the lowercase Greek letter used in mathematics, physics, and engineering to represent pi.