# PI

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&#960; is the mysterious number that most people think is merely 3.14. &#960; is the ratio of a circle’s circumference to its diameter. &#960; has been calculated to 206,158,430,000 digits, which was accomplished by Yasumasa Kanada and Daisuke Takahashi from the University of Tokyo in September of 1999. On the other hand, there were the Babylonians and Hebrews who lived and died, believing that &#960; was simply 3. Evidence from the Rhind papyrus shows that the Egyptians knew 3.16, but implied in their Great Pyramid is the even better value 3.14. Much like the Babylonians, the early Hindus and Chinese accepted 3. Archimedes led the Greeks to believe that the limits of &#960; were 3.141< &#960; <3.143. The later Greeks, with the knowledge of Ptolemy, knew 3.1416. In the 5th century A.D. Tsu Ch’ung-chih, a Chinese mechanician, gave &#960; correct to six decimals. This feat was not paralleled in the western world for 1000 years. Another common belief was that &#928; was the square root of ten, which was somehow equal to 3 1/7.
A little known verse from the Old Testament leads us to believe that the Hebrews used 3 as their value of Pi. “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 about, (I Kings 7, 23).” There is some speculation involved in this passage, as some say that the diameter of ten cubits was the measurement from one side to the next, whereas the thirty-cubit circumference was of the inner lining of the vessel. If the sides were about 0.2254 cubits thick, this would lead to decent value of pi.
Around 225 B.C., Archimedes obtained his incredibly accurate limits for &#960; with the perimeters of inscribed and circumscribed polygons having 96 sides. This was an extremely difficult task for Archimedes, as he didn’t have Arabic numerals to work with. Lacking Arabic numerals, he had much difficulty in computing the essential square roots square roots. Tsu Ch’ung-chih’s method is not known for sure, but may have been similar to Archimedes’. Following the path of polygon usage, in 1579 Francois Vieta used polygons of 393,216 sides to obtain &#960; to 9 correct places. This style came to an end in 1610, when the German eccentric Ludolph van Ceulen calculated &#960; to 35 places by means of a polygon with 4 quintillion, 611 quadrillion, 686 trillion, 18 billion, 427 million, 387 thousand, 904 sides.