what is the history of pi?

Answer 1

Pi is the ration of the circumfence of a circle to its diameter.

Pi = Circumference / Diameter

π = The character of symbol

π = 3.141592654. . . .

π = is non termination non repeating decimal

π = is irrational

I provided the following link for future reference

en.wikipedia.org/wiki/History_of_%CF%80

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Answer 2

Once upon a time, Greek mathematicians (legend says it was Pytagoras among others) tried to establish a relationship between the diameter of a pot and it's circumference.

Afetr many tries, it was for sure that it was about 3 and something, but, since no decimal s were known in that time (unless they could be represented as a rational number), this problem was announced unsolvable. An approximate value was found somehow, and it was 22/7, which was close enough for that time, but not precise.

Roman mathematicians, however, kept on dividing decimals and subsequently discovered that the ratio is not rational number. Couple of the first decimals are 1415926 ... which clearly shows that it is an indefinite series of decimals.

Since only first two decimals are of interest when performing calculations, the achieved accuracy was enough for many purposes, including engineering.

Later, when numerical analysis became of interest to the mathematicians (in 18th century) many of them tried to calculate the final decimal of the pi, in order to provide higher accuracy of calculations.

Today, computers have found milions of decimals, but it is not much of a news today, since we still perform all calculations with 3.14.

Answer 3

The mathematical constant π is an irrational real number, approximately equal to 3.14159, which is the ratio of a circle's circumference to its diameter in Euclidean geometry, and has many uses in mathematics, physics, and engineering. It is also known as Archimedes' constant (not to be confused with an Archimedes number) and as Ludolph's number.

[edit] Use of the symbol π
Often William Jones' book A New Introduction to Mathematics from 1706 is cited as the first text where the Greek letter π was used for this constant, but this notation became particularly popular after Leonhard Euler adopted it some years later (cf History of π).


[edit] Early approximations
Main article: History of numerical approximations of π
The value of π has been known in some form since antiquity. As early as the 19th century BC, Babylonian mathematicians were using π = 25⁄8, which is within 0.5% of the true value.

The Egyptian scribe Ahmes wrote the oldest known text to give an approximate value for π, citing a Middle Kingdom papyrus, corresponding to a value of 256 divided by 81 or 3.160.

It is sometimes claimed that the Bible states that π = 3, based on a passage in 1 Kings 7:23 giving measurements for a round basin as having a 10 cubit diameter and a 30 cubit circumference. Rabbi Nehemiah explained this by the diameter being measured from outside rim to outside rim while the circumference was the inner brim; but it may suffice that the measurements are given in round numbers.


Principle of Archimedes' method to approximate πArchimedes of Syracuse discovered, by considering the perimeters of 96-sided polygons inscribing a circle and inscribed by it, that π is between 223⁄71 and 22⁄7. The average of these two values is roughly 3.1419.

The Chinese mathematician Liu Hui computed π to 3.141014 in AD 263 and suggested that 3.14 was a good approximation.

The Indian mathematician and astronomer Aryabhata in the 5th century gave the approximation π = 62832⁄20000 = 3.1416, correct when rounded off to four decimal places. He also acknowledged the fact that this was an approximation, which is quite advanced for the time period.

The Chinese mathematician and astronomer Zu Chongzhi computed π to be between 3.1415926 and 3.1415927 and gave two approximations of π, 355⁄113 and 22⁄7, in the 5th century.

The Indian mathematician and astronomer Madhava of Sangamagrama in the 14th century computed the value of π after transforming the power series expansion of π⁄4 into the form


and using the first 21 terms of this series to compute a rational approximation of π correct to 11 decimal places as 3.14159265359. By adding a remainder term to the original power series of π⁄4, he was able to compute π to an accuracy of 13 decimal places.

The Persian astronomer Ghyath ad-din Jamshid Kashani (1350–1439) correctly computed π to 9 digits in the base of 60, which is equivalent to 16 decimal digits as:

2π = 6.2831853071795865
By 1610, the German mathematician Ludolph van Ceulen had finished computing the first 35 decimal places of π. It is said that he was so proud of this accomplishment that he had them inscribed on his tombstone.

In 1789, the Slovene mathematician Jurij Vega improved John Machin's formula from 1706 and calculated the first 140 decimal places for π, of which the first 126 were correct [1], and held the world record for 52 years until 1841, when William Rutherford calculated 208 decimal places of which the first 152 were correct.

The English amateur mathematician William Shanks, a man of independent means, spent over 20 years calculating π to 707 decimal places (accomplished in 1873). In 1944, D. F. Ferguson found that Shanks had made a mistake in the 528th decimal place, and that all succeeding digits were incorrect. By 1947, Ferguson had recalculated pi to 808 decimal places (with the aid of a mechanical desk calculator).

Answer 4

That is simple if you spell it Pi Man.

Answer 5

The history of pi is as follows.
History of π
From Wikipedia, the free encyclopedia
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The mathematical constant π = 3.14159... has been subject to extensive study since ancient times.

This article gives a historical account on the increasing human knowledge about its mathematical properties. Here the aim is not to focus on the precision of known numerical approximations. There are more specialized articles about

* the history of numerical approximations of π, which says more about the ongoing hunt for billions of decimal places of π
* the chronology of computations of π with an overview of "world records" concerning these computations.

Contents
[hide]

* 1 History of π
o 1.1 Theory
o 1.2 Computation
* 2 History of the notation
* 3 See also
* 4 Notes
* 5 References
* 6 External links

[edit] History of π

[edit] Theory

* That the ratio of the circumference to the diameter of a circle is the same for all circles, and that it is slightly more than 3, was known to ancient Egyptian, Babylonian, Indian and Greek geometers. The Indians and Greeks also knew that the area of a circle is πr2, where r is the radius.

* Archimedes showed that the volume of a sphere is (4/3)πr3, where r is the radius, and that the surface area of a sphere is 4πr2, i.e., 4 times the area of the circle with the same radius. (Also it is notable that the derivative of volume of a sphere is the formula for the surface area of a sphere.)

* The Indian mathematician and astronomer Madhava of Sangamagrama in the 14th century found the following infinite series expansion of π:

\frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots \pm \frac{1}{2n -1} \cdots

This can also be writen as follows:

\pi=4\left(1-\sum^\infty_{k=1} \frac{1}{2k}+\sum^\infty_{k=1} \frac{1}{2k+1}\right)

which is a realization of the power series expansion of the arctangent function. Madhava also used the first 21 terms of the related series:

\pi = \sqrt{12}\left(1-{1\over 3\cdot3}+{1\over5\cdot 3^2}-{1\over7\cdot 3^3}+\cdots\right)

to compute a finite-series approximation of π correct to 11 decimal places as 3.14159265359.

* In the 18th century, Abraham de Moivre found that when a fair coin is tossed 1800 times, the probability that the number of heads is x is approximately

C \exp\left({-(x-900)^2 \over 900}\right)

where C is a constant that de Moivre could compute by numerical means. (This normal distribution was introduced in the 1738 edition of de Moivre's book The Doctrine of Chances.) As the number of tosses grows, the approximation can be made as close as desired (but "900" would be replaced by a larger number). De Moivre's friend James Stirling later showed that this constant is

{1 \over \sqrt{2\pi}}.

* In 1761, Johann Heinrich Lambert showed that π is an irrational number by showing that tana is irrational if a is rational, and since tanπ / 4 = 1, it follows that π is irrational.

* In 1882, Ferdinand von Lindemann proved that π is a transcendental number. It had earlier been proved that if π is transcendental, then it is impossible to solve the ancient Greek geometers' problem of squaring the circle.

* In 1953, Kurt Mahler proved that π is not a Liouville number.

[edit] Computation

Main article: History of numerical approximations of π.

* The Egyptian scribe Ahmes wrote the oldest known text to give an approximate value for π, citing a Middle Kingdom papyrus, corresponding to a value of 256 divided by 81 or 3.160.
* As early as the 19th century BC, Babylonian mathematicians were using π = 25/8, which is within 0.53% of the exact value.
* By finding perimeters of circumscribed and inscribed regular polygons, Archimedes found that π is between 3 + 10/71 and 3 + 1/7.
* The Chinese mathematician Liu Hui computed π to 3.141014 (good to three decimal places) in AD 263 and suggested that 3.14 was a good approximation.
* According to I Ching (635–713), the Arc of 1/4 circle is 10, the chord is 9 so the pi is √2/0.9×2 = 3.1426968052735445…, while why the ratio of chord/Arc=0.9 is unknown.
* The Indian mathematician and astronomer Aryabhata in the 5th century gave the approximation π = 62832/20000 = 3.1416, correct when rounded off to four decimal places.
* The Chinese mathematician and astronomer Zu Chongzhi computed π to be between 3.1415926 and 3.1415927 and gave two approximations of π, 355/113 and 22/7, in the 5th century.
* In the 14th century, the Indian mathematician and astronomer Madhava of Sangamagrama used

\frac{n^2 + 1}{4n^3 + 5n}

as an approximation of the remainder term of the infinite series expansion of \frac{\pi}{4}, after summing the series through n = 75, to find a rational approximation of π that was correct to 13 decimal places of accuracy.

* In 1424, the Persian Muslim mathematician and astronomer Ghyath ad-din Jamshid Kashani (1380–1429) correctly computed 2π to 9 sexagesimal (base 60) digits.[1] This figure is equivalent to 16 decimal (base 10) digits as

\ 2\pi = 6.2831853071795865

which corresponds to

\ \pi = 3.14159265358979325

He achieved this level of accuracy by calculating the perimeter of a regular polygon with 3 × 218 sides.

* With the appearance of computers, a hunt on millions and billions of decimal places of π has started and is still ongoing. See history of numerical approximations of π for a detailed account.

[edit] History of the notation

The symbol "π" for Archimedes' constant was first introduced in 1706 by William Jones when he published A New Introduction to Mathematics, although the same symbol had been used earlier to indicate the circumference of a circle. The notation became standard after it was adopted by Leonhard Euler. In either case, 'π' is the first letter of περιφέρεια (periphereia, the Greek word for periphery) or περίμετρον (perimetron), meaning 'measure around' in Greek.

[edit] See also

* list of topics related to π
* List of formulae involving π
* history of numerical approximations of π
* chronology of computation of π

[edit] Notes

1. ^ Al-Kashi, author: Adolf P. Youschkevitch, chief editor: Boris A. Rosenfeld, p. 256

[edit] References

* A History of Pi, by Petr Beckmann, 1971, St. Martin's Griffin, ISBN 0312381859.
* The Crest of the Peacock, by George Ghevergese Joseph.

[edit] External links

* Records in the calculation of pi.
* Detailed chronology of record-breaking calculations. Retrieved October 22, 2005.
* The Life of Pi by Jonathan Borwein.
* Madhava of Sangamagramma.

Retrieved from "http://en.wikipedia.org/wiki/History_of_%CF%80"

Categories: History of mathematics | Pi

Answer 6

Here's your answer:
http://en.wikipedia.org/wiki/Pi

I hope that helps!

Answer 7

Have you not tried wikipedia?