Mar 14, 2008

Happy π Day!

A couple days ago I received this email in my inbox. I couldn't help but roll my eyes, but then at the same time laugh a little. Of course this email would come from a bunch of developers, right? I mean, who cares about the impending and much more well known "Ides of March" or "Saint Patrick's Day". In this business π is apparently a bigger deal. That being said, the historical part is very interesting to me....sorry, can't help it.

"This Friday is a little more important than your normal end of the week. March 14th is an important day, celebrated by millions around the world. Heralded as possibly the most significant number in human history by mathematicians the world over, March 14th is a day to celebrate the ratio of circle’s diameter to its circumference. The Project Manager has been kind enough to help support this holiday by providing some pie (and coffee) for us to enjoy. Please join us at 1:59 PM on Friday, March 14th, to help us celebrate this joyous important day. (3.14 1:59) 2pm is close enough!

The Number
π is an irrational number, a transcendental number, and is the basis for one the 3 classical mathematical problems: squaring the circle.

The History
Though it is sometimes credited to the ancient Egyptians, sometimes to Sumerians, or maybe the Babylonians, or the Hindus, or the Olmecs, the letter itself is Greek, coming from the Greek περίμετρος (perimeter) a term which is normally credited to Euclid in his integral mathematical text, Elements. π itself being used as a constant to represent the ratio was not used until 1706 by William Jones in A New Introduction to Mathematics. Euler’s adoption of this notation in 1737 popularized the notation which we still use today. Though there is much argumentation about which civilization should get the credit, the fact that so many of our ancient ancestors discovered π is proof enough of its historical significance.

Egypt first used the value 3, before refining it to a value of 256/81 (3.1605).
Babylonia used the approximation 25/8 (3.125)
India used 339/108 (3.138)
The best of the ancient approximations of π was Archimedes who realized the magnitude of π could be bounded from below and above by using inscribed circles. He realized π was between 223/71 and 22/7 giving the best approximation of 3.1419
Almost 600 years later, Zu Chongzhi, a Chinese mathematician gave the approximation 335/113 and that π is bounded by 3.1415926 and 3.1415927.
Chongzhi’s approximation stood for 900 years before calculus evolved in mathematics that allowed Madhava of Sangamagrama to discover the first known series which represents π. This was the first historical calculation of Pi accurate to more than 10 decimal places.
Only 20 years later, the Persian astronomer Jamshid al-Kashi correctly determined 16 digits.
The first European contribution since Archimedes was Ludolph van Ceulen to calculate 32 digits of π. So proud was he of this achievement that his tombstone bears his approximation.
Better and better approximations came until the best pre-computer calculation of 527 accurate digits by William Shanks, he had calculated 707, but it was later found his 528th digit was incorrect due to his inaccurate formula.
Finally Johann Heinrich Lambert proved π’s irrationality in 1761.
Due to use of computers John von Neumann calculated 2037 digits of π in 1949, this feat took 70 hours on ENIAC.
1973 finally had π accurate to a million decimal places.
In 1989 π was first calculated to a billion decimal places.
The current record is 1,241,100,000,000 decimals, set is 2002."

1 comment:

Nicole said...

I heard all about pi day on NPR today. The only thing I really got from the experience (besides being glad I am no longer in high school geometry)... I ended up craving some pie. I am not joking. I might have to go out and get some pecan or apple pie from the store tonight.