Pi

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Pi () is the ratio of the circumference of a circle to its diameter: approximately 3.14159 (but mathematicians have struggled for centuries to provide better and better approximations). Using the convention that Greek letters in mathematics have conventional meaning, the ratio takes its name from the sixteenth letter of the Greek alphabet. 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 approximate value of 3.14159 is precise enough for almost all ordinary purposes; it can, for example, be used to calculate the circumference of a circle of the size of the Earth with an error of only about 110 feet.

For rough purposes, the fraction 22/7 (= 3.142857...) 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.

Some ancients expressed 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[1]. 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 .[2] 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 .

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.[Citation Needed] That result was never printed out.

in mathematics

It's impossible to overestimate the importance of (and e) for mathematics. Both values are intrinsically tied, e.g. by Euler's identity

.

Recreation

Memorizing is a challenge that appeals to some people. Mnemonics have been devised. Counting the letters in each word of 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, 3/14, comes from the first three digits of ; some people begin their celebration at 1:59 pm, derived from the following three digits.

Approximation Day is a similar holiday, celebrated on July 22 (from the approximation 22/7). [3]

is approximately:

3.14159265358979323846264338327950288419​7169399375​1058209749​4459230781​6406286208​9986280348​2534211706​7982148086​5132823066​4709384460​9550582231​7253594081​2848111745​0284102701​9385211055​5964462294​8954930381​9644288109​7566593344​6128475648​2337867831​6527120190​9145648566​92...

Greek Language Usage

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

Does the Bible attempt to define ?

Virtually all serious students of the Bible say no. Still, critics frequently claim that the Bible contains an incorrect value for [4], and the question is raised frequently enough to earn mention in the Skeptics Annotated Bible.

The 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 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 . This is clearly not the case; it is merely describing the size of the object.[5]
  • The value in the Bible is wrong, rather than just imprecise. However, to the nearest whole number, the value is correct,[5] and it was quite common at the time to round numbers.[6] For instance the value of 10 could actually be any value between 9.5 and 10.5. If it was to the lower end of that range, then the equation works.
  • 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.[6]
  • 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.[7]

However, even if the claim is correct, rounding to 3 is not "incorrect," an "error" or "wrong" and is perfectly acceptable in some circumstances.[8] The creation of a "sea of cast metal" by human beings (not God) in ancient times without modern construction tools and measuring equipment is easily understood as one of those circumstances.

Bibliography

See Also

References