Difference between revisions of "Pi"
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(Remove Meekrok's change. In my opinion, it would indeed imply that Pi=3 _if_ it was meant to be taken literally, but let's not guess at what was meant) |
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For rough purposes, the fraction 22/7 (= 3.14285...) is sometimes used. | For rough purposes, the fraction 22/7 (= 3.14285...) is sometimes used. | ||
| − | + | 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. 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: can you figure out why not? | |
| − | + | In the Bible, 1 Kings 7:23 contains the famous 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." This quotation predates Greek mathematics and is an example of the wisdom contained in the bible. | |
| − | == | + | Papyrys of Ahmes, dated c. 1650 B.C.E. circa 1000 years before Book of Kings, shows that ancient Egyptians had value 3 1/6 = 3.166666667, which is significantly closer to biblical value. Same goes with Babylonian value from same time <big><math>\pi</math></big> 3 1/8 = 3.125(Boyer, A History of Mathematics, 2nd Edition). |
| − | + | 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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[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 00:23, March 13, 2007
Pi is the name for the Greek letter <math>\pi</math>, which corresponds to the English letter p.
<math>\pi</math> is also the symbol used in mathematics for the ratio between the diameter of a circle and its circumference, and which appears in many other places.
<math>\pi</math> is an irrational number; this means that it cannot be expressed as a fraction, and (therefore) cannot be expressed exactly as a decimal no matter how many decimal places it is carried out to.
The value of <math>\pi</math> is approximately 3.14159. 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 350 feet.
For rough purposes, the fraction 22/7 (= 3.14285...) is sometimes used.
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 <math>\pi</math> has been calculated. In 1873 Abraham Shanks spent twenty years calculating <math>\pi</math> to 707 places, but unfortunately made a mistake in his calculation and only 527 of them were correct. When electronic computers were developed, <math>\pi</math> 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: can you figure out why not?
In the Bible, 1 Kings 7:23 contains the famous 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." This quotation predates Greek mathematics and is an example of the wisdom contained in the bible.
Papyrys of Ahmes, dated c. 1650 B.C.E. circa 1000 years before Book of Kings, shows that ancient Egyptians had value 3 1/6 = 3.166666667, which is significantly closer to biblical value. Same goes with Babylonian value from same time <math>\pi</math> 3 1/8 = 3.125(Boyer, A History of Mathematics, 2nd Edition).
Memorizing <math>\pi</math> 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 <math>\pi</math> 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 Near a Raven which simultaneously parodies Edgar Allen Poe's poem The Raven, while encoding <math>\pi</math> to 740 places.