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A Brief History of Pi

People have been aware of pi since Bible times, and although it is impossible to discover exacticly who excatly was the first to notice that the ratio of the circumfrance to the diameter of a circle is always slightly over three, we do know about most of the dicoveries made regarding pi, and their approximent years. I don't have room to list all of them, but here are the most importent discoveries:

  • 2000 B.C - Babylonians use pi = "3 1/8".
  • 263 - Liu Hui uses "157/50 = 3.14".
  • 530 - Aryabhata uses "62,832/20,000".
  • 650 - Brahmagupta uses "sqr 10".
  • 1220 - Leonardo de Pisa (Fibonacci) finds "3.141818..."
  • 1593 - Francois Viete finds first infinite series.
  • 1593 - Adrian Romanus finds 15 decimal places.
  • 1596 - Ludolph Van Ceulen calculates 32 places; in 1610, expands it to 35.
  • 1665-66 - Sir Isaac Newton discovers calculus and calcuates pi to at least 16 decimal places, not published until 1737.
  • 1699 - Abraham Sharp calculates 72 decimal places.
  • 1706 - John Machin calculates 100 places
  • 1706 - William Jones institutes the symbol for pi.
  • 1761 - Johann Heinrich Lambert proves the irrationality of pi.
  • 1794 - Georg Vega (yes, this is the correct spelling) calculates 140 decimal places.
  • 1844 - L.K. Schulz von Stassnitzky and Johann Dase calculate 200 places in under two months.
  • 1855 - Richter calculates 500 decimal places.
  • 1873-1874 - William Shanks publishes his 707 digits.
  • 1882 - Ferdinand von Lindemann proves the transcendence of pi.
  • 1945 - D.F. Ferguson finds Shanks's Calculation wrong starting at the 527th digit.
  • 1947 - Ferguson calculates 808 places using a desk calculator in about a year.
  • 1949 - ENIAC (a computer) calculates 2,037 decimal digits in seventy hours.
  • 1955 - MORC (a computer) calculates 3,089 decimal digits in thirteen minutes.
  • 1959 - IBM 704 (a computer) calculates 16,167 decimal digits.
  • 1967 - CDC 6600 (yet another computer) calculates 500,000 digits.
  • Jean Guiloud and M. Bouyer use a CDC 7600 (Paris) to extract 1,000,000 digits.
  • 1988 - Kanada computes 201,326,000 digits on a Hitachi S-820 in 6 hours.
  • 1995 - Kanada computes 6 billion digits.
  • 1997 - Kanada and Takahashi calcuate 51.5 billion digits in just over 29 hours on a Hitachi SR2201.

Comon Pi Formulas
Pi = ...

  • c/d ; A/r2
  • 4arctan1
  • 4(4arctan1/5 - arctan1/239)
  • 4(2arctan1/3 + arctan1/7)
  • 4(5arctan1/7 + 2arctan3/79)
  • 4(4arctan1/5 - arctan1/70 + arctan1/99)
  • 4(45/[360/2Pi])
  • sqr {6 [1/(12) + 1/(22) + 1/(32)]}
  • sqr {6 [22/(22-1) * 32/(32-1) * 52/(52-1) * 72/(72-1) * 112/(112-1) * ...]}
  • cuberoot {32 [1/(13) - 1/(33) + 1/(53) - 1/(73) ...]}
  • fourthroot {90 [1/(14)+ 1/(24) + 1/(34) + ...]}
  • 2(3/2*5/6*7/6*11/10*13/14*17/18*19/18*23/22*...)
  • sqr(12Li2[1/2] + 6[ln2]2)
  • 5arccosPhi/2 (or, by inserting the formula for Phi...) 5 * arccos([sqr5]/2+.5)/2 -- [I derived this formula algebraicly from a similar one for Phi]
  • arccos(-1) -- [My own discovery!]
Note: All calculations must be done in Radians. You can do this merely by taking the answer in Degrees, and multiplying it by 2Pi/360, or about: 57.295779513082320876798154814105170332405472466564321... (However, you will want to limit how many decimals you use based on how accurate you wish your calculation to be. Just take the number of decimal places you want plus 2, for calculator rounding safety.) The reasoning behind this conversion is simple: There are 2*pi Radians in a circle (Radians are like Degrees, only not broken up into as many parts; Radians, in fact, was created to involve pi in the number of parts a circle is broken up into), therefore the Degrees to Radians ration is 360:2pi. So you can multiply your degrees by (2*pi)/360 to get radians, or your radians by 360/(2*pi). So an example of degrees to radians would be: 127 * (2*pi/360). An example of the converse, radians to degrees, would be: pi/5 * (360/2*pi). Note: Radians are often expressed with pi, i.e.: pi/5 or (2*pi)/3. Also, for your ease, you can reduce the 2*pi:360 ratio to just pi/180. Be sure to use this fractional form in your multiplying if you wish for an exact answer. See my downloads for calculators to aid you in these calculations.

Odd Pi Facts

  • The world cacluation record currently is 1.241 trillion decimal places. If you lined up all of these digits in about font 14, it would reach from the Earth to the moon.
  • The world PC calculation record currently is 25 billion decimal places.
  • If you lined up one billion digits, they would stretch from Washington D.C. to Las Vegas.
  • If you take the third, sixth, and nineth digits, they are, respectivly, 1,2,3.
  • If you take the 100th, 200th, and 300th digits, they are, resectivly, 9,6,3.
  • The sequence 333 is found three times in the first 7,000 digits.
  • The sequence 666 is found six times in the first 7,000 digits.
  • Only 20 decimal digits are neccessary to calculate the circumfrance of the Earth down to a fraction of an inch.
  • Only 39 decimal digits are neccessary to calculate the circumfrance of the known universe down to the electron.
  • "Pi" is the sixteenth character of the Greek alphabet, and "p" is the sixteenth of ours.
  • If you "multiply" pi times "e" you get "pie".... (get it?)
  • Savannah, Georgia has a zip code of 31415.