Difference between revisions of "Pi"

Revision as of 12:47, March 13, 2008

Pi is the sixteenth letter of the Greek alphabet and is used in its lower case form () 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 mathematical and physical formulae.

The value of 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).

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 about 110 feet.

For rough purposes, the fraction 22/7 (= 3.14285...) is sometimes used.

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 ancient world it was common, and often sufficient, to express the relationship between the circumference of a circle and its diameter as an integer ratio, 3:1. For example, 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." One of the less serious arguments made against Biblical inerrancy is that the 3:1 ratio does not permit a precise calculation of the value of pi. Many counterarguments exist^[1][2], including the fact that pi is irrational (and hence impossible to represent exactly in decimal or fractional form), as well as the observation that nowhere does the Bible set out to provide its readers with the values of mathematical constants.

Some ancients expressed pi more precisely by using fractional approximations. Papyrus of Ahmes, dated c. 1650 B.C., shows that ancient Egyptians had value 3 1/6 = 3.167). The Babylonian value from the same era was 3 1/8 = 3.125^[3]. Both these values are accurate to within 1 percent. Note that the value 22/7 (3 1/7) is still used today.

Archimedes of Syracuse (287-212 BC) carried out "the first theoretical calculation" of pi.^[4] He said it was between 223/71 and 22/7. This is ten times better than the Egyptian and Babylonian values: within 0.04% of pi.

In 1873, Abraham Shanks spent twenty years calculating to 707 places, but 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). ^[5]

Greek Language Usage

This letter's name is pronounced the same as its equivalent in English (P) and has the same sound value.

Pi in the Bible

Bible critics frequently claim that the Bible has an incorrect value for Pi. This claim is based on a verse in the first book of Kings:

He made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it. 1_Kings 7:23 (NIV)

The critics say that this amounts to the Bible claiming that the value of pi is 3.

There are a number of assumptions involved in making this claim, and if any one of the assumptions is wrong, the claim is false. The assumptions are:

• The Bible is trying to provide a value for pi. This is clearly not the case; it is merely describing the size of the object.^[6]
• The value in the Bible is wrong, rather than just imprecise. However, to the nearest whole number, the value is correct,^[6] and it was quite common at the time to round numbers.^[7]
• That both the diameter and the circumference are measuring the same edges. It's possible, even if unlikely, that the diameter is an outside measurement and the circumference is an inside measurement. A straight calculation doesn't allow for the thickness of the sides.^[7]
• That both the diameter and the circumference are measuring the same part of the object. The object is also described as having an outward-turned rim. The easiest places to measure the diameter would be across the wider rim, and the easiest place to measure the circumference would be around the body below the rim.^[8]

See Also

• Pi day
• Calculation of pi with computers

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. ↑ Rounding was standard procedure in the ancient world. Is the Bible Wrong About Pi?
3. ↑ Boyer, A History of Mathematics, 2nd Edition
4. ↑ Pi through the ages
5. ↑ USA Today (3/14/2007) - Pi-day
6. ↑ ^{6.0 6.1} Peterson and Rick, 1999.
7. ↑ ^{7.0 7.1} Holding, J.P.
8. ↑ Grigg, 1995.

External links

• Holding, James Patrick, Pi Gets In Your Eye (Tektonics).
• Grigg, Russell, Does the Bible say pi equals 3.0? Creation 17(2):24–25, March 1995.
• Peterson & Rick, Rouding Pi 1st June(?), 1999 (The Math Forum).