Subject: radical numbers
What Is Pi?
Pi is lots of things. Pi is the 16th letter of the Greek alphabet, which corresponds to the English letter "p". Since the Greek word for circumference was something like "periphery", it was therefore natural for the Greeks to use this letter to stand for the circumference of a circular region, in particular, for the CIRCUMFERENCE OF A CIRCLE WHOSE RADIUS IS 1/2.
Euclid (around 300 BC) showed that pi equals the ratio of the circumference of a circle to its diameter. Today we use this as the definition of the number we call pi.
Archimedes (around 250 BC) proved the remarkable fact that pi also equals the area of the unit circle (or what's more useful, pi equals the ratio of the area of a circle to the square of its radius; in other words, (area of circle) = pi * r 2). He then showed how to compute pi to any desired degree of accuracy, namely 3.14159265... .
The whole story is told in the book, THE HISTORY OF PI, by Petr Beckmann.
A couple of other places to look are The Pi Home Page and the symbols and constants list at The Earliest Uses of Various Mathematical Symbols.
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