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| − | '''Pi''' is the sixteenth letter of the [[Greece|Greek]] [[alphabet]] and is used in its lower case form (<big><math>\pi</math></big>) to represent the mathematical constant of the same name which is defined as ''the ratio of the circumference of a circle to its diameter''. It is an important number and appears in many [[mathematics|mathematical]] and [[physics|physical]] formulae.
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| − | The value of <big><math>\pi</math></big> is an [[irrational number]]; which means that it cannot be fully expressed as a fraction or a decimal (regardless of the number of digits used).
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| − | The value of <big><math>\pi</math></big> is approximately 3.14159 in decimal. This value is precise enough for almost all ordinary purposes; it can, for example, be used to calculate the circumference of the Earth with an error of only about 110 feet.
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| − | For rough purposes, the fraction 22/7 (= 3.14285...) is sometimes used while 355/113 (=3.1415929...) is accurate to six places.
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| − | In hexadecimal (base-16) notation, <big><math>\pi</math></big> is approximately 3.243f.
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| − | ==History==
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| − | To some extent, the progress of mathematics—or at least of computation—can be gauged by the progress in the number of digits to which <big><math>\pi</math></big> has been calculated.
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| − | In the Bible, 1 Kings 7:23 contains the passage "And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about." Making many assumptions<ref>Assuming that: the "sea" is perfectly circular; the measurements are to be understood as exact; the measurement of the "compass" and across the "brim" are measurements of the same circle, rather, than say, exterior and interior measurements of a wide lip; etc.</ref> this quotation (which predates Greek mathematics) would appear to equate Pi to 3.
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| − | Papyrus of Ahmes, dated c. 1650 B.C. circa 1000 years before Book of Kings, shows that ancient Egyptians had value 3 1/6 = 3.166666667. The Babylonian value from same time <big><math>\pi</math></big> 3 1/8 = 3.125<ref>Boyer, A History of Mathematics, 2nd Edition</ref>.
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| − | In 1873, Abraham Shanks spent twenty years calculating <big><math>\pi</math></big> to 707 places, but unfortunately made a mistake in his calculation and only 527 of them were correct. When electronic computers were developed, <big><math>\pi</math></big> was soon calculated to tens of thousands, millions, and billions of places. As of 2002, the record is held by Yasumasa Kanada of Tokyo University at 1,241,100,000,000 digits. That result was never printed out.
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| − | ==Recreational use==
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| − | Memorizing <big><math>\pi</math></big> is a challenge that appeals to some people. Mnemonics have been devised. Counting the letters in the phrase "Now I want a drink—alcoholic, of course" gives <big><math>\pi</math></big> to seven places (which is more than enough for all ordinary purposes). Numerous other mnemonics of this kind have been devised; in 1995, Michael Keith wrote one entitled [http://users.aol.com/s6sj7gt/mikerav.htm Near a Raven] which simultaneously parodies [[Edgar Allen Poe]]'s poem ''The Raven,'' while encoding <big><math>\pi</math></big> to 740 places.
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| − | March 14 marks Pi Day, a holiday on which the mathematical constant is celebrated. The date comes from the first three digits of pi; some people begin their celebration at 1:59 pm, derived from the following three digits.
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| − | Pi Approximation day is a similar holiday, celebrated on July 22 (from the approximation 22/7). <ref>[http://www.usatoday.com/tech/science/mathscience/2007-03-14-pi-day_N.htm USA Today (3/14/2007) - Pi-day]</ref>
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| − | == Greek Language Usage ==
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| − | This letter's name is pronounced the same as its equivalent in English (P) and has the same sound value.
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| − | ==Notes and references==
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| − | <references/>
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| − | [[Category:Mathematics]]
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