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.
