The History of Pi By Joel Chorny Phys 001 Spring 2004
Pi is ancient “The fact that the ratio of the circumference to the diameter of a circle is constant has been known for so long that it is quite untraceable” (O’Connor). The Bible contains a verse that tells us a value of pi that was used. “And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and its height was five cubits: and a line of thirty cubits did compass it about”- (I Kings 7, 23) Here the value of pi is given as 3, not very accurate, not even for its time.
Even the Egyptian and Mesopotamian values of 25/8= 3.125 and √10= 3.162 have been traced to much earlier dates than the biblical value of 3 The earliest values of pi were almost certainly empirically determined, which means they were found by measurement. Rhind Papyrus
Pi becomes theoretical It appears to have been Archimedes who was the first to obtain a theoretical calculation of pi. He concluded the following: 223/71<pi<22/7 Archimedes used inequalities very sophisticatedly here to show that he knew pi did not equal 22/7. He never claimed to have found the exact value. It has become one of the most prominent missions of the scientific community to calculate pi more and more precisely
Pi becomes more and more exact Ptolemy calculated pi to be 3.1416 Zu Chongzhi obtained the value pi= 355/113 Al-Khwarizmi without knowledge of Ptolemy’s work found pi to be 3.1416 Al-Kashi calculated pi to 14 decimal places Roomen calculated pi to 17 decimal places Van Ceulen calculated pi to 35 decimal places
Al-Khwarizmi Lived in Baghdad Gave his name to the word “algorithm” The word “algebra” comes from al jabr, the title of one of his books Was the pioneer of the calculation of pi in the East Al-Khwarizmi
The art of calculating Pi evolves Complex formulas are developed in the European Renaissance to calculate pi. With these formulas available, the difficulty in calculating pi comes only in the sheer time consumption and boredom of continuing the calculation. This task is much like Napier’s when he decided to determine the value for logarithms.
Some people were “dedicated” enough to actually spend incredible amounts of time and effort continuing the calculation of pi. 1699: Sharp gets 71 correct digits 1701: Machin gets 100 digits 1719: de Lagny gets 112 correct digits 1789: Vega gets 126 places 1794: Vega gets 136 places 1841: Rutherford gets 152 digits 1853: Rutherford gets 440 digits 1873: Shanks calculates 707 places of which 527 were correct
Detailed Chronology of the Calculation of pihttp://www-groups.dcs.st-and.ac.uk/~h
Augustus de Morgan English mathematician born in India Looked at Shanks’ 707- digit calculation of pi. Noticed that there was a suspicious shortage of 7s. In 1945 Ferguson discovers that Shanks had made a mistake in the 528th place, which lead to all the following digits to be wrong. De Morgan
More precision becomes available Pi was calculated to 2000 places with the use of a computer in 1949. In this calculation, and all calculations following it, the number of 7s does not differ significantly from its expectation. The record number of decimal places for pi calculated in 1999 was 206,158,430,000. However, this record has already been broken.
The Notation of pi The first to use the symbol π with its current meaning was William Jones in 1706. He was a William Jones Welsh mathematician. Euler adopted the symbol in 1737 and it soon became a standard. Leonhard Euler
What does all this have to do with us?Throughout the semester we have beenlearning about how improvements havebeen made in the art of measurement.Tyco Brahe used instruments the size ofbuildings to take accurate measurementsof the movement of the stars and planets.The constant attempt to improve on ourunderstanding of pi is similarly to be ableto make more accurate measurements.
Just as scientists have tried to calculatethe speed of light to the most accuratedecimal possible, scientists are trying todefine pi to the most accurate decimal. Itis becoming increasingly often that pi isdefined in terms of more decimal places
If you want to get a sense of how huge the amount of decimal places calculated for pi is, go to the following url (Load time is pretty long): http://3.1415926535897932384626433832795
Source UsedO’Connor, J. J. and E. F. Robertson. “A History of Pi.” Aug. 2001. University of St. Andrews. 27 Apr. 2004 <http://www-history.mcs.st- andrews.ac.uk/HistTopics/Pi_through_the_ages.html>.