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Pi

π (sometimes written pi) is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in Euclidean space; this is the same value as the ratio of a circle's area to the square of its radius. It is approximately equal to 3.141593 in the usual decimal notation (see the table for its representation in some other bases). The constant is also known as Archimedes Constant, although this name is rather uncommon in modern, western, English-speaking contexts. Many formulae from mathematics, science, and engineering involve π, which is one of the most important mathematical and physical constants. π is an irrational number, which means that its value cannot be expressed exactly as a fraction m/n, where m and n are integers. Consequently, its decimal representation never ends or repeats. It is also a transcendental number, which implies, among other things, that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) can be equal to its value; proving this was a late achievement in mathematical history and a significant result of 19th century German mathematics. Throughout the history of mathematics, there has been much effort to determine π more accurately and to understand its nature; fascination with the number has even carried over into non-mathematical culture. The Greek letter π, often spelled out pi in text, was adopted for the number from the Greek word for perimeter "περίμετρος", first by William Jones in 1707, and popularized by Leonhard Euler in 1737. The name of the Greek letter π is pi, which is the English equivalent of the Greek name πι.[7] The English name is commonly used in typographical contexts when the Greek letter is not available or its usage could be problematic.[citation needed] As a mathematical symbol, it is not capitalized (Π) even at the beginning of a sentence.[clarification needed] When referring to this constant, the symbol π is always pronounced /ˈpaɪ/,[citation needed] "pie" in English, which is the conventional English pronunciation of the Greek letter. In Greek, the name of this letter is pronounced [pi]. The constant is named "π" because "π" is the first letter of the Greek words περιφέρεια (periphery) and περίμετρος (perimeter), probably referring to its use in the formula to find the circumference, or perimeter, of a circle. π is Unicode character U+03C0 ("Greek small letter pi"). Note:Pi has more than 10 thousand decimals. Well before computers were used in calculating π, memorizing a record number of digits had become an obsession for some people. In 2006, Akira Haraguchi, a retired Japanese engineer, claimed to have recited 100,000 decimal places. This, however, has yet to be verified by Guinness World Records. The Guinness-recognized record for remembered digits of π is 67,890 digits, held by Lu Chao, a 24-year-old graduate student from China. It took him 24 hours and 4 minutes to recite to the 67,890th decimal place of π without an error.[58] On June, 17th, 2009 Andriy Slyusarchuk, a Ukrainian neurosurgeon, medical doctor and professor claimed to have memorized 30 million digits of pi, which were printed in 20 volumes of text. Although he did not recite the entire 30 million digits that he claims to have memorized, media claim that he was able to recite any randomly selected sequences from the printed text of the 30 million digits. There are many ways to memorize π, including the use of "piems", which are poems that represent π in a way such that the length of each word (in letters) represents a digit. Here is an example of a piem, originally devised by Sir James Jeans: How I need (or: want) a drink, alcoholic in nature (or: of course), after the heavy lectures (or: chapters) involving quantum mechanics. Notice how the first word has 3 letters, the second word has 1, the third has 4, the fourth has 1, the fifth has 5, and so on. The Cadaeic Cadenza contains the first 3835 digits of π in this manner. Piems are related to the entire field of humorous yet serious study that involves the use of mnemonic techniques to remember the digits of π, known as piphilology. In other languages there are similar methods of memorization. However, this method proves inefficient for large memorizations of π. Other methods include remembering patterns in the numbers and the method of loci.