Wednesday, May 23, 2012

Pi Pi Pi

3.14159265358979323846264338327950288419716939975105, you have just read 51 digits of one of the most famous numbers in the world. Pi is number of times the diameter of a circle wraps around its circumference. Pi can also be used to find the area of a circle. If you multiply the radius of a circle squared by pi, you get the area of that circle.
         Pi didn’t just fall out of the sky one day, it was stumbled upon. The Egyptians and Babylonians are credited for discovering pi over four thousand years ago. One theory on how they discovered pi is that they simply made a big circle, and measured how many time the diameter measured around the circumference. Their ratio however, was slightly miscalculated. They proposed that pi was three and one eight, which would be three point one two five.
         The next evidence of pi is found in the bible of all places, Kings seven twenty three says, “Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about". This says he made a circle, 10 cubits in diameter, and 30 cubits around. This states that the circumference is three times the diameter, so pi equals three
         After that, the Greeks took up the problem. Antiphon and Bryson of Heraclea thought of the idea of putting a shape inside a circle, then doubling the sides over and over again, and measuring the area. They thought that a shape with enough sides would be a circle, like a dodecagon, with twenty sides, looks almost exactly like a circle unfortunately, a dodecagon is not a circle, so they could only get a few numbers.
         The next discovery was one of the greatest. Archimedes of Syracuse decided to start where Antiphon and Bryson left off, but instead of using the area of the polygon, he used the perimeter. He started with a hexagon, and doubled its sides four times, making a ninety-six sided polygon. Then Archimedes used a special method that is very hard to understand, it includes something called trigonometric notation.

         It wasn’t until 236 AD the next breakthrough happened. Liu Hui used Bryson and Antiphon’s idea, and created a one hundred ninety-two sided shape. Hui found the first six digits of pi, 3.14159.
         After that, the next discovery wasn’t until the fifteen hundreds. A French mathematician named Francle viete used Archimedes method with two hexagons, and doubling the number of sides sixteen times, to finish with three hundred ninety-three thousand two hundred sixteen sides. He proposed that pi was between 3.1415926535, and 3.1415926537. The first number was correct, but more importantly, he pioneered the idea that pi was irrational and therefore infinite. Viete then discovered seven more digits, but the last two digits were wrong.
         Only three years later, a German named Ludolph Ceulen presented 20 correct digits of pi, using Archimedes strategy, with a polygon with over five hundred million sides. He spent most of his life finding more digits, by the time he died, he had accurately calculated thirty five digits. His discoveries were so extraordinary, that those 35 digits are carved in his tombstone.
         It has taken three and a half thousand years to find a little more than half of the digits that I have memorized!
         In 1706, John Machin, an astronomer in London, made a formula to find more digits in pi. This still very complex formula enabled Machin to find one hundred digits by hand.
         The domino effect followed the discovery. In 1873, William Shanks calculated 707 digits, but in total 527 digits were correct. It took until 1949 to find the next digits to be found. A group of mathematician fed punch cards into a huge super computer of the time, to get 2037 digits. Then, John Wrench and Daniel Shanks found 100,000 digits in 1961, one million was discovered in ’73.
         It is impossible to remember and almost impossible to imagine the immenseness of the number of digits we have found. As of 1999 the record for most calculated digits is 68 billion 719 million, 470 thousand. Of course we don’t need that many digits, just 39 digits can calculate the circumference of a circle around the universe. I guess curiosity that drives us to find even more pi.

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