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Eta Bita Pi: One Of The World's Most Interesting Numbers

Mar 31, 2008
Circles are odd things. We encounter them all the time in nature - in fact we couldn't exist without them, the earth and all its heavenly neighbors (including the sun) being spherical - and yet mathematicians and geometers insist that there are no perfect circles, outside the realm of theory.

Circles turn up in mythology, religion, literature, and culture - pagan religions insist on the importance of "sacred circles," while in Eastern Orthodox Christianity the Trinity is sometimes conceived of as Father, Son and Holy Spirit dancing in an eternal circle. And it turns out that the search for a proper definition of a circle's characteristics has sent mathematicians and scientists on a search lasting, at this writing, thousands of years, with no sign of letting up.

Pi is the traditional name for the number that represents the ratio of a circle's circumference (the distance all the way around it) to its diameter (the length of a line straight across its middle). The relationship between these two numbers - the circumference and the diameter - is always the same, no matter how big or small the circle used to do the measuring; therefore pi is always the same number.

The problem is that this number can't really be written. For convenience sake, people often say that pi is 3.14159, but in fact the digits continue after that decimal point - into the millions and billions of numbers, past the current computing capacity of the human race. It seems to continue forever. So far as scientists have been able to discover, its digits never fall into any recurring or regular patterns. (A proof by the mathematician Johann Lambert, from 1768, showed that such patterns can't be.)

We're not sure who was the first person (or people) to try to calculate pi, but the Egyptians and the Babylonians both seem to have been aware of its importance. (They thought it was "a little more than three" - perhaps, as one Babylonian text suggests, 3 and one-eighths.) Study of the number slowed after the Greeks figured it at around 3.14; the Greeks had no system of decimals, which makes this achievement all the more impressive.

At this point progressed stalled until the Enlightenment, when scores of mathematicians working with nothing more than pencil and paper calculated pi up to around 1000 digits. Newton's and Leibniz's discovery of calculus offered mathematicians a chance to compute pi with greater accuracy.

The twentieth century brought another quantum leap in the history of the study of pi. First, mathematicians discovered mathematical formulae that allowed much better calculation of pi than was possible before. The Indian mathematician Ramanujan had discovered such a formula by 1910. But no matter how powerful your mathematical formulae, there's only so much you can do with pencil and paper, and so the other major development of the twentieth century allowed for fuller use of these significant new formulae.

Computers, with their amazing, well, computing power, gave mathematicians a chance to see more of pi than previous generations could have imagined. For example, in 1985 Ramanujan's formula was used to yield a 17-million-digit computation of pi. At the moment, the record for calculating pi is 51 billion decimal places. So what's all the fuss about?

The Egyptians and Babylonians used pi in architecture - for example, the Egyptians needed it to calculate the volume, or storage potential, of a cylindrical silo for storing grain. But pi continues to offer possibilities as practical as the number is mysterious. Engineers use pi to do line-of-sight calculations for fighter jets; it's used in manufacturing to craft circular parts for machines.

Radio, TV, radar and other wave-emitting communication devices pose problems involving pi - some waves (called "sine waves") have periods (or lengths) of 2 times pi, so the number imposes itself on any efforts to process signals, for example, or to perform spectrum analysis (figuring out the frequencies of the waves in messages you receive), among other things. Statisticians use pi to figure probability. And, of course, since the earth is circular, pi offers many advantages to navigators.

A long-distance flight, for example, involves a flight over a particular arc of a circle (the globe), and that factor must be included when doing calculations to figure out exactly how much fuel and other resources will be used during the flight. And you need pi just to figure out your location on the globe!
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