Facts about Pi – 3.14 … (03-14-2008, pi day)
Video Title: Maths Pi Song
Video Desc: Pi Song
Video Desc: Pi Song
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Info: March 14 -- 3-14 -- 3.14 -- pi ; A mathematical holiday celebrating the number pi (3.1415926535897932384626433832795028841 9...).
Info: March 14 -- 3-14 -- 3.14 -- pi ; A mathematical holiday celebrating the number pi (3.1415926535897932384626433832795028841 9...).
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- The Babylonians are credited as having recorded the first value for Pi (around 2000 BCE) and they used (25 / 8).
- The earliest known reference to Pi is on a Middle Kingdom papyrus scroll, written around 1650 BC by Ahmes the scribe.
- In around 200 BC Archimedes found that Pi was between (223/71) and (22/7). His error was no more than 0.008227 %. He did this by approximating a circle as a 96 sided polygon.
- Ludolph Van Ceulen (1540 – 1610) spent most of his life working out Pi to 35 decimal places. Pi is sometimes known as Ludolph’s Constant
Another name for Pi in Germany is ‘die Ludolphsche Zahl’ after Ludolph van Ceulen, the German mathematician who devoted his life to calculating 35 decimals of pi. - In 1706 William Jones first gave the Greek letter Ï€ its current mathematical definition.
The first person to use the Greek letter Pi was Welshman William Jones in 1706. He used it as an abbreviation for the periphery of a circle with unit diameter. Euler adopted the symbol and it quickly became a standard notation. - A rapidly converging formula for calculation of Pi found by Machin in 1706 was:
pi/4 = 4 * arctan (1/5) – arctan (1/239). - In 1768 Johann Lambert proved Pi is irrational.
Pi is irrational. An irrational number is a number that cannot be expressed in the form (a / b) where a and b are integers. - In 1882 Ferdinand Lindemann, proved the transcendence of Pi.
Pi is a transcendental number. (Transcendental means= Not capable of being determined by any combination of a finite number of equations with rational integral coefficients.) This means that it is not the solution to any finite polynomial (eg: lots of numbers added in a series) with whole number coefficients. This is why it is impossible to square the circle. - It is easy to prove that if you have a circle that fits exactly inside a square, then pi = 4 times (Area of circle) / (Area of square)
- If one were to find the circumference of a circle the size of the known universe, requiring that the circumference be accurate to within the radius of one proton only 39 decimal places of Pi would be necessary.
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