story of pi

The history of pie : 

The history of pie (Futile is the labor of those who fatigue themselves with calculations to square the circle.)- Michael Stifel (1544)

Slide 2: 

Made by - Devbrath gupta X-C Roll no. -12

What is pi ? : 

What is pi ? By definition, pi is the ratio of the circumference of a circle to its diameter. Pi is always the same number, no matter which circle you use to compute it.

What is pi represented as? : 

What is pi represented as? To make it easy people sometimes round pi. For many purposes you can use 3.14159, which is good, but if you want a better approximation you can use a computer to get it.

What’s the formula?? : 

What’s the formula?? The area of a circle is pi times the square of the length of the radius, or "pi r squared": A = pi*r^2

The history of pi : 

The history of pi Pi is a very old number. We know that the Egyptians and the Babylonians knew about the existence of the constant ratio pi, although they didn't know its value nearly as well as we do today. They had figured out that it was a little bigger than 3; the Babylonians had an approximation of 3 1/8 (3.125), and the Egyptians had a somewhat worse approximation of 4*(8/9)^2 (about 3.160484), which is slightly less accurate and much harder to work with.modern day technology allows us to calculate pi to billions of decimal places. 3.14 is usually all we need.

About Pi : 

About Pi Pi is an infinite decimal. Unlike numbers such as 3, 9.876, and 4.5, which have infinite nonzero numbers to the right of the decimal place, pi has infinitely many numbers to the right of the decimal point. If you write pi down in decimal form, the numbers to the right of the 0 never repeat in a pattern. Some infinite decimals do have patterns - for instance, the infinite decimal .3333333... has all 3's to the right of the decimal point, and in the number .123456789123456789123456789... the sequence 123456789 is repeated. However, although many mathematicians have tried to find it, no repeating pattern for pi has been discovered

Why try to prove pi is rational : 

Why try to prove pi is rational But why would anyone want to calculate beyond the first few digits? The ten digits (3.141592654) that are in most scientific calculators are good enough for almost any real-world calculation; you can calculate the circumference of the Earth's orbit around the sun, and be off by less than 100 meters.

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Chronology - The most significant events in the history of piYear                                                        Achievement 2000 B.C.E.                                Babylonians use p = 25/8 = 3.125. 2000 B.C.E.                                Egyptians use p = 256/81 = 3.1605. 1100 B.C.E.                                Chinese use p = 3. 550 B.C.E.                               Old Testament implies p = 3. 434 B.C.E.                               Anaxagoras attempts to square the circle. 430 B.C.E.                               Antiphon and Bryson articulate the principle of exhaustion. 335 B.C.E.                               Dinostratos uses the quadratix to "square the circle". 250 B.C.E.                               Archimedes uses a 96-sided polygon to establish 223/71 < p < 22/7. He also uses a spiral to square the circle. 150                               Claudius Ptolemy uses p = 3°8'30" = 377/120 = 3.14166.... 250                               Wang Fau uses p 142/45 = 3.1555.... 263                               Liu Hui uses p = 157/50 = 3.14. 450                               Tsu Ch'ung-chih establishes 355/113. 530                               Aryabhata uses p = 62832/20000 = 3.1416. 650                               Brahmagupta uses p = 10 1/2 = 3.162.... 1220                               Leonardo de Pisa (Fibonacci) finds p = 3.141818.... 1593                               François Viète finds first infinite product to describe pi. 1593                               Adrian Romanus finds pi to 15 decimal places. 1596                               Ludolph Van Ceulen calculates pi to 32 places. 1610                               Van Ceulen expands calculation to 35 decimal places. 1621                               Willebrod Snell refines the Archimedean method. 1654                               Huygens proves the validity of Snell's refinement.

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1655                               John Wallis finds an infinite rational product for pi. 1655                               Brouncker converts it to a continued fraction. 1663                               Muramatsu Shigekiyo finds seven accurate digits in Japan. 1666                               Isaac Newton discovers calculus and calculates pi to at least 16 decimal places; not published until 1737 (posthumously). 1671                               James Gregory discovers the arctangent series. 1674                               Gottfried Wilhelm Leibniz discovers the arctangent series for pi. 1699                               Abraham Sharp calculates pi to 72 decimal places. 1706                               John Machin calculates pi to 100 places. 1706                               William uses the symbol p to describe the circle ratio. 1713                               Chinese court publishes 'Su-li Ching-yun', which shows pi to 19 digits. 1719                               Thomas Fantet de Lagny calculates pi to 127 decimal places. 1722                               Takebe Kenko finds 40 digits in Japan. 1748                               Leonhard Euler publishes the 'Introduction in analysin infinitorum', containing Euler's theorem and many series for p and p 2 . 1755                               Euler derives a very rapidly converging arctantgent series. 1761                               Johann Heinrich Lambert proves the irrationality of pi. 1775                               Euler suggests that pi is transcendental. 1794                               Georg Vega calculates pi to 140 decimal places. 1794                               A.M. Legendre proves the irrationality of p and p 2 .

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1844                               L.K. Schulz von Stassnitzky and Johann Dase calculate pi to 200 places in under two months. 1855                               Richter calculates pi to 500 decimal places. 1873                               Charles Hermite proves the transcendence of e. 1874                               William Shanks publishes his calculation of pi to 707 decimal places. 1874                               Tseng Chi-hung finds 100 digits in China. 1882                              Ferdinand von Lindemann proves the transcendence of pi. 1945                               D. F. Ferguson finds Shanks' calculation wrong from the 527 th place 1959                               IBM 704 (Paris) computes 16167 decimal places. 1961                               Daniel Shanks and John Wrench use IBM 7090 (New York) to compute 100200 decimal places in 8.72 hours. 1966 IBM 7030 (Paris) computes 250000 decimal places. 1967                               CDC 6600 (Paris) computes 500000 decimal places. 1973 Jean Guilloud and M. Bouyer use a CDC 7600 (Paris) to compute 1 million decimal places in 23.3 hours. 1983                               Y. Tamura and Y. Kanada use a HITAC M-280H to compute 16 million digits in under thirty hours. 1988 Kanada computes 201326000 digits on a Hitachi S-820 in six hours. 1989                               Chudnovsky brothers find 480 million digits. 1989                               Kanada calculates 536 million digits. 1989                               Chudnovskys calculate 1 billion digits. 1995                               Kanada computes 6 billion digits. 1996                               Chudnovsky brothers compute over 8 billion digits. 1997 Kanada and Takahashi calculate 51.5 billion (3 × 2 34 ) digits on a Hitachi SR2201 in just over 29 hours. 1999                               Kanada and Takahashi calculate 68,719,470,000 digits.

What makes PI so damn cool? : 

What makes PI so damn cool? Mathematicians have longed for a method to prove that pi is a never-ending, random sequence of numbers. The constant has been calculated to 500 billion decimal places and no pattern has been found. If mathematicians are right, no pattern will ever be found, and proving this would be a breakthrough in our understanding of numbers. Proving pi to be random, though, proves very difficult.