The history of PI (part I)
62Archimedes the first who has demonstrated the value of PI
Archimedes (285-212 B.C. ?) used a very sophisticated process for his time to achieve the calculus of PI since of course algebraic and trigonometrical notations were unknown.
His approach consisted of inscribing and circumscribing regular polygons with many sides in and around the circle, and computing the perimeter of these polygons. This provided him with an upper and a lower bound for pi.
More precisely, he considered a circle of radius 1, in which he inscribed a regular polygon of 3 cross 2n-1 sides, with semiperimeter bn, and superscribe a regular polygon of 3 cross 2n-1 sides, with semiperimeter an.
The effect of this procedure is to define an increasing sequence b1 , b2 , b3 , ... and a decreasing sequence a1 , a2 , a3 , ... such that both sequences have limit PI.
But PI seems to be known since the Phoenicians at least
In the Old Testament Bible or Jewish Torah it was said:
"And he [Hiram the Phoenician hired by King Solomon to design the building of the Jewish temple] made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty cubits did compass it round about....And it was an hand breadth thick...." — First Kings, chapter 7, verses 23 and 26
According to some site like purplemath, this shows the Phoenicians (1200 BC to 900 BC) did know about the number PI.
No progress was made until European Renaissance
Except for Zu Chongzhi (429–500 AD) a Chinese mathematician and astronomer who introduced the approximation 355/113 to p which is correct to 6 decimal places, there had been no theorical progress until the European Renaissance.
During that time several Mathematicians discovered arithmetical formulas for Pi:
Wallis (1616-1703) discovered that:
2/p = (1.3.3.5.5.7. ...)/(2.2.4.4.6.6. ...)
Though often attributed to Leibniz, of the best-known formula has been discovered by James Gregory:
p/4 = 1 - 1/3 + 1/5 - 1/7 + ....
The discovery that PI is irrational and transcendental
"An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q" (from Wolfram Mathworld). PI was proved to be irrational by Lambert (1728 - 1777).
A transcendental number means there is no ruler and compass to build by geometric rules a square equal in area to a given circle. PI was proved to be transcendental by Lindemann (1852 - 1939).
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I'm sorry for making you remembering it :)
by the way whats the current numbers of decimals place calculated in pi so far?
Anansi, to answer your question:
Aided by a supercomputer, a University of Tokyo mathematician set the world record for figuring out pi to 1.24 trillion decimal places in 2002.
2002.
Radannsun 4 years ago
Believe it or not, my professor wanted us to explain Archimedes' method of reaching pi. I will be glad to be out of the class. *Brain begins to hurt at the memory of it.