PI

Pinyin Bi, in art, Chinese jade carved in the form of a flat disk with a hole in the centre. The earliest examples, which are unornamented, date from the Neolithic period (c. 30001500 BC). Later examples, from the Shang dynasty (18th12th century BC) and the Chou dynasty (1111255 BC), have increasingly elaborate surface embellishment, especially in the late Chou (c. 600255 BC), when the pi appears in combination with other forms. The pi may have been a symbol of heaven or of the Sun (in that it resembles the ancient graph for sun). in mathematics, the symbol p denoting the ratio of the circumference of a circle to its diameter. The ratio is approximately 3.14159265, pi being an irrational number (one that cannot be expressed as a ratio of two whole numbers or as a decimal with a repeating pattern of digits) and a transcendental number (a real number that is not an algebraic numberthat is, a real number that is not the solution of any polynomial equation with rational coefficients). Computers in the late 20th century carried pi to more than 100,000,000 decimal places. Pi occurs in various mathematical calculations. The circumference (c) of a circle can be determined by multiplying the diameter (d) by p: c = pd. The area (A) of a circle is determined by the square of the radius (r): A = pr2. Pi is applied to mathematical problems involving the lengths of arcs or other curves, the areas of elipses, sectors, and other curved surfaces, and the volumes of solids. It is also used in various formulas of physics and engineering to describe such periodic phenomena as the motion of pendulums, the vibration of strings, and alternating electric currents. In very ancient times, 3 was used as the approximate value of pi, and not until Archimedes (3rd century BC) does there seem to have been a scientific effort to compute it; he reached a figure equivalent to about 3.14. A figure equivalent to 3.1416 dates from before AD 200. By the early 6th century Chinese and Indian mathematicians had independently confirmed or improved the number of decimal places. By the end of the 17th century in Europe, new methods of mathematical analysis provided various ways of calculating pi. Early in the 20th century the Indian mathematical genius Srinivasa Ramanujan developed ways of calculating pi that were so efficient that they have been incorporated into computer algorithms, permitting expressions of pi in millions of digits.