## Pi

π pi is a letter of the Greek alphabet but it is most known as the symbol for the mathematical  number of the ratio of a circle circumference to its diameter. An animation showing the relationship of the circumference and diameter. image: wikipedia

The number π is a mathematical constant, the ratio of a circle's circumference to its diameter, approximately equal to 3.14159.

also C = 2πr, where r = radius or d/2

It has been represented by the Greek letter "π" since the mid-18th century though it is also sometimes spelled out as "pi" (/paɪ/).

Being an irrational number, π cannot be expressed exactly as a common fraction, although fractions such as 22/7 and other rational numbers are commonly used to approximate π.

2,000 decimal places of pi. data source

Consequently its decimal representation never ends and never settles into a permanent repeating pattern. The digits appear to be randomly distributed although no proof of this has yet been discovered.

Also, π is a transcendental number – a number that is not the root of any nonzero polynomial having rational coefficients. This transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straight-edge.

For thousands of years mathematicians have attempted to extend their understanding of π, sometimes by computing its value to a high degree of accuracy.

Before the 15th century mathematicians such as Archimedes and Liu Hui used geometrical techniques, based on polygons, to estimate the value of π. Starting around the 15th century, new algorithms based on infinite series revolutionized the computation of π.

Computing pi

In the 20th and 21st centuries mathematicians and computer scientists discovered new approaches that, when combined with increasing computational power, extended the decimal representation of π to, as of late 2011, over 10 trillion (1013) digits.

Scientific applications generally require no more than 40 digits of π so the primary motivation for these computations is the human desire to break records. However, the extensive calculations involved have been used to test supercomputers and high-precision multiplication algorithms.

Applications of pi in maths and science

Because its definition relates to the circle, π is found in many formulae in trigonometry and geometry, especially those concerning circles, ellipses or spheres.

It is also found in formulae used in other branches of science such as cosmology, number theory, statistics, fractals, thermodynamics, mechanics and electromagnetism.

Pi is popular

The ubiquity of π makes it one of the most widely-known mathematical constants both inside and outside the scientific community: Several books devoted to it have been published, the number is celebrated on Pi Day and record-setting calculations of the digits of π often result in news headlines. Attempts to memorize the value of π with increasing precision have led to records of over 67,000 digits.

Here is a nice video providing a brief history of Pi