PI - 6 reference results
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 31/7, 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 eiπ=-1, where i=-1.
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Licensed from Columbia University Press
Licensed from Columbia University Press
Pi-hahiroth, in the Bible, place in Egypt, between Migdol and Baal-zephron, where the Israelites encamped.
The Columbia Electronic Encyclopedia Copyright © 2004.
Licensed from Columbia University Press
Licensed from Columbia University Press
Pi y Margall, Francisco, 1824-1901, Spanish statesman and writer. A liberal journalist, he fled to France after the unsuccessful uprising of 1866 against Gen. Leopoldo O'Donnell. After the overthrow of Isabella II in 1868 he was elected (1869) to the Cortes. He was briefly president (1873) of the short-lived first Spanish republic, and he continued as deputy in the Cortes after the restoration of the monarchy (1875). He defended the principle of federalism against centralism, thus gaining wide popularity in Catalonia and also among the anarchists. He also favored autonomy for Cuba. His uprightness and intelligence won him the respect even of the hostile right.
The Columbia Electronic Encyclopedia Copyright © 2004.
Licensed from Columbia University Press
Licensed from Columbia University Press
In mathematics, the ratio of the circumference of a circle to its diameter. An irrational number (seealso 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.
Learn more about pi with a free trial on Britannica.com.
Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
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