History of Pi

Topics: Pi, Circle, Daniel Shanks Pages: 9 (3413 words) Published: June 21, 2012
The History of Pi

Throughout the history of mathematics, one of the most enduring challenges has been the calculation of the ratio between a circle's circumference and diameter, which has come to be known by the Greek letter pi. From ancient Babylonia to the Middle Ages in Europe to the present day of supercomputers, mathematicians have been striving to calculate the mysterious number. They have searched for exact fractions, formulas, and, more recently, patterns in the long string of numbers starting with 3.14159 2653..., which is generally shortened to 3.14. William L. Schaaf once said, "Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number pi" (Blatner, 1). We will probably never know who first discovered that the ratio between a circle's circumference and diameter is constant, nor will we ever know who first tried to calculate this ratio. The people who initiated the hunt for pi were the Babylonians and Egyptians, nearly 4000 years ago. It is not clear how they found their approximation for pi, but one source (Beckman) makes the claim that they simply made a big circle, and then measured the circumference and diameter with a piece of rope. They used this method to find that pi was slightly greater than 3, and came up with the value 3 1/8 or 3.125 (Beckmann, 11). However, this theory is probably a fantasy based on a misinterpretation of the Greek word "Harpedonaptae," which Democritus once mentioned in a letter to a colleague. The word literally means "rope-stretchers" or "rope-fasteners." The misinterpretation is that these men were stretching ropes in order to calculate circles, while they were actually making measurements in order to mark the property limits and areas for temples, according to (Heath, 121).

A famous Egyptian piece of papyrus gives us another ancient estimation for pi. Dated around 1650 BC, the Rhind Papyrus was written by a scribe named Ahmes. Ahmes wrote, "Cut off 1/9 of a diameter and construct a square upon the remainder; this has the same area as the circle" (Blatner, 8). In other words, he implied that pi = 4(8/9)2 = 3.16049, which is also fairly accurate. Word of this did not spread to the East, however, as the Chinese used the inaccurate value pi = 3 hundreds of years later.

Chronologically, the next approximation of pi is found in the Old Testament. A fairly well known verse, 1 Kings 7:23, says: "Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about" (Blatner, 13). This implies that pi = 3. Debates have raged on for centuries about this verse. According to some it was just a simple approximation, while others say that "... the diameter perhaps was measured from outside, while the circumference was measured from inside" (Tsaban, 76). However, most mathematicians and scientists neglect a far more accurate approximation for pi that lies deep within the mathematical "code" of the Hebrew language. In Hebrew, each letter equals a certain number, and a word's "value" is equal to the sum of its letters. Interestingly enough, in 1 Kings 7:23, the word "line" is written Kuf Vov Heh, but the Heh does not need to be there, and is not pronounced. With the extra letter , the word has a value of 111, but without it, the value is 106. (Kuf=100, Vov=6, Heh=5). The ratio of pi to 3 is very close to the ratio of 111 to 106. In other words, pi/3 = 111/106 approximately; solving for pi, we find pi = 3.1415094... (Tsaban, 78). This figure is far more accurate than any other value that had been calculated up to that point, and would hold the record for the greatest number of correct digits for several hundred years afterwards. Unfortunately, this little mathematical gem is practically a secret, as compared to the better known pi = 3 approximation.

When the Greeks took up the problem, they took two revolutionary steps to...
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