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History of Pi

History of Pi. By Julian Wolf. 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)

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History of Pi

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  1. History of Pi By Julian Wolf

  2. 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

  3. 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

  4. 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.

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

  6. 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

  7. 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.

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

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