The Knowledge that there is a set ratio between the circumference of a circle and its diameter has been known for so long that its origins can't possibly be traced. References to this ratio appear in many places in the ancient world. The Egyptians used a value of Pi which is described in the Rhind Papyrus as 3.16, and this is dated as far back as 1650 BC. An ancient Babylonian tablet from c. 1900-1680 BC shows a value for Pi which is 3.125. A reference is even made in the bible (I Kings 7, 23), where the value of Pi is approximated to 3.
The first person that we know of to theoretically calculate values of Pi was Archimedes.
This Picture was taken from http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Archimedes.html
His value was an approximation, but if an average is taken it is found to be 3.1418. This is very accurate considering his technique, which can be found in my calculations of Pi section.
Using his technique any people calculated Pi to further decimal places:
|
Ptolemy |
c. 150 AD | |
|
al-Khwarizmi |
c. 800 | |
|
al-Kashi |
c. 1430 | |
|
Vičte |
1540-1603 | |
|
Roomen |
1561-1615 | |
|
Van Ceulen |
c. 1600 |
35 d.p |
In 430-501 AD a value of 355/113 was also found independently by Tsu Ch'ung Chi
This remained pretty much it until the European Renaissance. Wallis (1646-1716) was one of the first in this period to define Pi as an algebraic sequence:
2/p = (1.3.3.5.5.7. ..)/(2.2.4.4.6.6. ..)
Very soon after, James Gregory (1638- 1675) developed a second, now well known progression:
p/4 = 1 - 1/3 + 1/5 - 1/7 + ..
James Gregory, (worlds scariest man)
this picture was taken from http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Gregory.html
These two take a very long time to converge however, (10000 progression to get 4 d.p's), and so more work needed to be done. Gregory showed that this progression can be refined until a general rule for a quick convergence can be found. This was defined to be:
p/4 = tan-1(1/a) + tan-1(1/b)
Gregory used the values of 1/2 and 1/3 but in 1706 Machin found the far more accurate values of 1/5 and 1/239. His new formula was:
p/4 = 4 tan-1(1/5) - tan-1(1/239)
This series of progressions sparked a whole bunch of fanatics to calculate Pi to a huge number of decimal places. Lagny calculated 112 d.p, Vega got 136, Rutherford got 440, Shanks thought he got 707. (See the blunders section). In 1873 Lindemann proved that Pi is not the solution to any polynomial with integer coefficients.
Since the invention of computers able to repeat calculations with total accuracy over and over the number of decimal places of Pi has sky rocketed to ridiculous heights. The first was carried out in 1947 by Ferguson who on a desk top calculator managed to find correctly 710 digits. The most recent was done by Yasumasa Kanada and Daisuke Takahashi. (See the crazy stuff section).
Tenuous link: Tweety Pie
Taken from http://www.scally.com/tweety without permission