pi (redirected from Pi (number))

pi, in mathematics, the ratio of the circumference of a circle to its diameter. The symbol for pi is π. The ratio is the same for all circles and is approximately 3.1416. It is of great importance in mathematics not only in the measurement of the circle but also in more advanced mathematics in connection with such topics as continued fractions, logarithms of imaginary numbers, and periodic functions. Throughout the ages progressively more accurate values have been found for π; an early value was the Greek approximation 3 1-7, found by considering the circle as the limit of a series of regular polygons with an increasing number of sides inscribed in the circle. About the mid-19th cent. its value was figured to 707 decimal places and by the mid-20th cent. an electronic computer had calculated it to 100,000 digits. It would have taken a person working without error eight hours a day on a desk calculator 30,000 years to make this calculation; it took the computer eight hours. Although it has now been calculated to more than 200,000,000,000 digits, the exact value of π cannot be computed. It was shown by the German mathematician Johann Lambert in 1770 that π is irrational and by Ferdinand Lindemann in 1882 that π is transcendental; i.e., cannot be the root of any algebraic equation with rational coefficients. The important connection between π and e, the base of natural logarithms, was found by Leonhard Euler in the famous formula e^iπ=−1, where i=−1.

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pi

In mathematics, the ratio of the circumference of a circle to its diameter. An irrational number (see also transcendental number), it has an approximate value of 3.14, but its exact value must be represented by a symbol, the Greek letter π. Pi is used in calculations involving lengths, areas, and volumes of circles, spheres, cylinders, and cones. It also arises frequently in problems dealing with certain periodic phenomena (e.g., motion of pendulums, alternating electric currents). By the end of the 20th century, computers had calculated pi to more than 200 billion decimal places.

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pi

The 16th letter of the Greek alphabet. It is used as a symbol for the ratio of the circumference of a circle to its diameter, which is 3.141592653, commonly rounded to 3.14. Perhaps no other number has been more pondered, examined and calculated than pi. Circa 1650 B.C., the ratio was computed by an Egyptian scribe, and the number was recorded as 3.16049 in the Rhind Papyrus. The writings described how to create a square area the same size as a circle.

The Exact Value of Pi
Over the years, pi, which was named some 3,000 years later, has been calculated numerous times to the maximum decimal place that humans and calculating devices could take it. In 1596, it was calculated to 32 decimal places and up to 127 places by 1719. In 1949, the ENIAC took 70 hours to yield 2,037 digits. However, in 1997, a Hitachi mainframe computed pi to 51.5 billion digits in 29 hours. The bottom line is that the absolutely exact value of pi cannot be computed.

The Pi Symbol

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pi

1. the 16th letter in the Greek alphabet (Π, π), a consonant, transliterated as p

2. Maths a transcendental number, fundamental to mathematics, that is the ratio of the circumference of a circle to its diameter. Approximate value: 3.141 592…; symbol: π

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PI - An interface between Prolog application programs and the X Window System that aims to be independent from the Prolog engine, provided that it has a Quintus foreign function interface (e.g. SICStus and YAP). It is mostly written in Prolog and is divided in two libraries: Edipo - the lower level interface to the Xlib functions; and Ytoolkit - the higher level user interface toolkit. ftp://ftp.ncc.up.pt/pub/prolog/ytoolkit.tar.Z. E-mail: Ze' Paulo Leal <zp@ncc.up.pt>.