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History of Pi By Julian Wolf

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Babylonian Pi The ratio of the circumference to the diameter of a circle is constant (namely, pi) has been recognized for as long as we have written records. Ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius (pi=3) On one Babylonian tablet from ca 1680 bce gives pi a value of 3.125

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Egyptian Pi Ancient Egyptians calculated the area of a circle by using this formula. (d= diameter) This means the value of pi is 3.1605

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Archimedes’ Pi The first theoretical calculation of pi was done by Archimedes of Syracuse (287- 212 bce) He figured that 223/71 <pi< 22/7. His results were based off based on the area of a regular polygon inscribed within the circle and the area of a regular polygon within which the circle was circumscribed.

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Archimedes Cont. By starting with a hexagon he was able go all the way up to a 96 sided polygon. Called a : Called a : Enneacontakaihexag on

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European Pi Early European mathematicians such as James Gregory (1638-1675) developed new formulas. His was pi/4 = 1 - 1/3 + 1/5 - 1/7 +...... The only problem with this formula is that you add millions of terms to find the value of pi/4 that extends to 6 or 7 decimal places

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European Pi cont. In 1706 John Machin improved Gregory’s formula, which is still used today to program pi on computers. By using this formula William Shanks calculated pi to 707 places but only 527 places were right.

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The Symbol Itself Introduced by William Jones in 1706 he wrote : 3.14159 = pi 3.14159 = pi This symbol was adopted by Euler in 1737 and is still the standard symbol today.

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