Difference between revisions of "Pi"

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(113 ÷ 355 is easy to remember: 11 33 55)
(113 / 355 is not pi, it is its reciprocal)
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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 350 feet.  
 
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 350 feet.  
  
For rough purposes, the fraction 22/7 (= 3.14285...) is sometimes used. 113 ÷ 355 (= 3.14159292) is accurate to six places.
+
For rough purposes, the fraction 22/7 (= 3.14285...) is sometimes used. 355/113 is accurate to six places.
  
 
In hexadecimal (base-16) notation, <big><math>\pi</math></big> is approximately 3.243f.
 
In hexadecimal (base-16) notation, <big><math>\pi</math></big> is approximately 3.243f.

Revision as of 22:01, 28 March 2007

Pi is the name for the Greek letter , which corresponds to the English letter p.

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.

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 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 350 feet.

For rough purposes, the fraction 22/7 (= 3.14285...) is sometimes used. 355/113 is accurate to six places.

In hexadecimal (base-16) notation, is approximately 3.243f.

History

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 has been calculated.

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[1] this quotation (which predates Greek mathematics) would appear to equate Pi to 3.

Papyrys 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 3 1/8 = 3.125[2].

In 1873 Abraham Shanks spent twenty years calculating to 707 places, but unfortunately made a mistake in his calculation and only 527 of them were correct. When electronic computers were developed, 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.

Recreational use

Memorizing 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 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 to 740 places.

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.

Pi Approximation day is a similar holiday, celebrated on July 22 (from the approximation 22/7). [1]

Notes and references

  1. 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.
  2. Boyer, A History of Mathematics, 2nd Edition