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The History of

In the long history of the number , there have been many twists and turns, many

inconsistencies that reflect the condition of the human race as a whole. Through each

major period of world history and in each regional area, the state of intellectual thought,the state of mathematics, and hence the state of , has been dictated by the same socio-

economic and geographic forces as every other aspect of civilization. The following is a

brief history, organized by period and region, of the development of our understanding ofthe number .

In ancient times, was discovered independently by the first civilizations to begin

agriculture. Their new sedentary life style first freed up time for mathematical pondering,

and the need for permanent shelter necessitated the development of basic engineeringskills, which in many instances required a knowledge of the relationship between the

square and the circle (usually satisfied by finding a reasonable approximation of ).

Although there are no surviving records of individual mathematicians from this period,

historians today know the values used by some ancient cultures. Here is a sampling ofsome cultures and the values that they used: Babylonians - 3 1/8, Egyptians - (16/9)^2,

Chinese - 3, Hebrews - 3 (implied in the Bible, I Kings vii, 23).

The first record of an individual mathematician taking on the problem of (often called"squaring the circle," and involving the search for a way to cleanly relate either the area

or the circumference of a circle to that of a square) occurred in ancient Greece in the

400's B.C. (this attempt was made by Anaxagoras). Based on this fact, it is not surprisingthat the Greek culture was the first to truly delve into the possibilities of abstractmathematics. The part of the Greek culture centered in Athens made great leaps in the

area of geometry, the first branch of mathematics to be thoroughly explored. Antiphon,

an Athenian philosopher, first stated the principle of exhaustion (click on Antiphon formore info). Hippias of Elis created a curve called the quadratrix, which actually allowed

the theoretical squaring of the circle, though it was not practical.

In the late Greek period (300's-200's B.C.), after Alexander the Great had spread Greek

culture from the western borders of India to the Nile Valley of Egypt, Alexandria, Egyptbecame the intellectual center of the world. Among the many scholars who worked at the

University there, by far the most influential to the history of was Euclid. Through thepublishing ofElements, he provided countless future mathematicians with the tools withwhich to attack the problem. The other great thinker of this time, Archimedes, studied

in Alexandria but lived his life on the island of Sicily. It was Archimedes who

approximated his value of to about 22/7, which is still a common value today.

Archimedes was killed in 212 B.C. in the Roman conquest of Syracuse. In the years afterhis death, the Roman Empire gradually gained control of the known world. Despite their

http://help_window%28%27clazomenae.html%27%29/http://help_window%28%27antiphon.html%27%29/http://help_window%28%27antiphon.html%27%29/http://help_window%28%27hippias.html%27%29/http://help_window%28%27euclid.html%27%29/http://help_window%28%27archimedes.html%27%29/http://help_window%28%27clazomenae.html%27%29/http://help_window%28%27antiphon.html%27%29/http://help_window%28%27hippias.html%27%29/http://help_window%28%27euclid.html%27%29/http://help_window%28%27archimedes.html%27%29/

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other achievements, the Romans are not known for their mathematical achievements. The

dark period after the fall of Rome was even worse for . Little new was discovered about

until well into the decline of the Middle Ages, more than a thousand years afterArchimedes' death. (For an example of at least one mediaeval mathematician, see

Fibonacci.)

The History of (cont.)

While activity stagnated in Europe, the situation in other parts of the world was quitedifferent. The Mayan civilization, situated on the Yucatan Peninsula in Central America,

was quite advanced for its time. The Mayans were top-notch astronomers, developing a

very accurate calendar. In order to do this, it would have been necessary for them to havea fairly good value for . Though no one knows for sure (nearly all Mayan literature was

burned during the Spanish conquest of Mexico), most historians agree that the Mayan

value was indeed more accurate than that of the Europeans. The Chinese in the 5thcentury calculated to an accuracy not surpassed by Europe until the 1500's. The

Chinese, as well as the Hindus, arrived at in roughly the same method as the Europeans

until well into the Renaissance, when Europe finally began to pull ahead.

During the Renaissance period, activity in Europe began to finally get moving again.Two factors fueled this acceleration: the increasing importance of mathematics for use in

navigation, and the infiltration of Arabic numerals, including the zero (indirectly

introduced from India) and decimal notation (yes, the great mathematicians of antiquitymade all of their discoveries without our standard digits of 0-9!). Leonardo Da Vinci and

Nicolas Copernicusmade minimal contributions to the endeavor, but Franois Vite

actually made significant improvements toArchimedes' methods. The efforts ofSnellius,Gregory, and John Machin eventually culminated in algebraic formulas for that allowedrapid calculation, leading to ever more accurate values of during this period.

In the 1700's the invention of calculus by Sir Isaac Newton and Leibniz rapidly

accelerated the calculation and theorization of . Using advanced mathematics,Leonhard

Eulerfound a formula for that is the fastest to date. In the late 1700's Lambert (Swiss)and Legendre (French) independently proved that is irrational. Although Legendre

predicted that is also transcendental, this was not proven until 1882 when Lindemann

published a thirteen-page paper proving the validity of Legendre's statement. Also in the18th century, George Louis Leclerc, Comte de Buffon, discovered an experimental

method for calculating . Pierre Simon Laplace, one of the founders of probability theory,

followed up on this in the next century. Click here to learn more about Buffon's andLaplace's method.

Starting in 1949 with the ENIAC computer, digital systems have been calculating to

incredible accuracy throughout the second half of the twentieth century. Whereas ENIAC

was able to calculate 2,037 digits, the record as of the date of this article is206,158,430,000 digits, calculated by researchers at the University of Tokyo. It is highly

http://help_window%28%27fibonacci.html%27%29/http://help_window%28%27fibonacci.html%27%29/http://help_window%28%27davinci.html%27%29/http://help_window%28%27copernicus.html%27%29/http://help_window%28%27copernicus.html%27%29/http://help_window%28%27viete.html%27%29/http://help_window%28%27viete.html%27%29/http://help_window%28%27archimedes.html%27%29/http://help_window%28%27archimedes.html%27%29/http://help_window%28%27snellius.html%27%29/http://help_window%28%27gregory.html%27%29/http://help_window%28%27machin.html%27%29/http://help_window%28%27euler.html%27%29/http://help_window%28%27euler.html%27%29/http://help_window%28%27euler.html%27%29/http://library.thinkquest.org/C0110195/history/buffon.htmlhttp://library.thinkquest.org/C0110195/history/buffon.htmlhttp://help_window%28%27fibonacci.html%27%29/http://help_window%28%27davinci.html%27%29/http://help_window%28%27copernicus.html%27%29/http://help_window%28%27viete.html%27%29/http://help_window%28%27archimedes.html%27%29/http://help_window%28%27snellius.html%27%29/http://help_window%28%27gregory.html%27%29/http://help_window%28%27machin.html%27%29/http://help_window%28%27euler.html%27%29/http://help_window%28%27euler.html%27%29/http://library.thinkquest.org/C0110195/history/buffon.htmlhttp://library.thinkquest.org/C0110195/history/buffon.html

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probable that this record will be broken, and there is little chance that the search for ever

more accurate values of will ever come to an end.

Uses of

Ever wondered when you were going to use that annoying symbol outside of mathclass? Well then this section is for you. Besides knowing that is Circumference divided

by diameter, it's also important to actually be able to use the thing. Use this section to

learn the basics of pi, then go on to the Applications of message boardand see whatother people have said about how they use .

Fun with

So you want to have some fun, huh? Well, you've come to the right place. Here you can

try a wordsearch, or, if that's not your style, try ourmadlib and put your gargantuan

vocabulary to use. When you're in the mood for a little bit of extra fun, we have a poem

modeled after the best of the best, Shakespeare himself. Read it here

An Ode to " or

"A Mathematician's Fantasy"~A Shakespearean Sonnet~

by Bryan Beyer

Oh , every night I think of you,

Your perfect circles wander through my dreams.I would like to deny it, but its true,

Forever I will adore you, it seems.

Squares just can't shape up; triangles are lame.

A heptagon is just too hard to draw,Each hexagon looks exactly the same.

But I will not forget the time I sawThat enchanting ratio in your eyes.

Your diameter to circumference

Will never change, would not dare to surprise,

And that, dear , makes all the difference.I commit you to my heart evermore-

Alas, my , you are three-point-one-four.

Euclidean geometry, attributed by Greek mathematician Euclid (born 325 BC) was thefirst recorded system used to show Pi as a mathematical constant. Pi is approximately

equal to 3.14159, which is also referred to the constant circumference. William Jones

used the name Pi for the Greek letter meaning the perimeter in 1706, and at a later time

http://library.thinkquest.org/C0110195/cgi-bin/forum.cgi?sec=appofpihttp://library.thinkquest.org/C0110195/cgi-bin/forum.cgi?sec=appofpihttp://library.thinkquest.org/C0110195/fun/pipuz.htmlhttp://library.thinkquest.org/C0110195/fun/irrationalform.htmlhttp://library.thinkquest.org/C0110195/fun/irrationalform.htmlhttp://library.thinkquest.org/C0110195/fun/ode.htmlhttp://library.thinkquest.org/C0110195/fun/ode.htmlhttp://library.thinkquest.org/C0110195/cgi-bin/forum.cgi?sec=appofpihttp://library.thinkquest.org/C0110195/fun/pipuz.htmlhttp://library.thinkquest.org/C0110195/fun/irrationalform.htmlhttp://library.thinkquest.org/C0110195/fun/ode.html

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referred more often by Leonhard Euler.

Although in 5th century Aryabhatt calculate the circumference of the earth and that timehe used 22/7 as constant in the calculation. But that value was not assigned to any

character, as Euclid did.

Who discovered Pi? Well if it had to be accredited to one person it would have to be

Euclid.===pi (symbol p). In geometry pi has been defined historically in two different ways,

although in both cases as the numerical value of a ratio associated with the circle. The

ratio of the circumference of any circle to its diameter is always the same. The ratio of

the area of any circle to that of the square on its radius is also always a constant, andperhaps surprisingly it also has the same value as the previous ratio. The Sumerians, in

3000 BC, knew of this ratio and calculated it to be approximately 3. It is in fact both an

irrational number and a transcendental number, nowadays commonly approximated by

3.142 or 22/7. It has been evaluated to billions of decimal places by computer. Althoughthe symbol p was used during the 17th century, it was its use by Euler* in 1737 which

promoted its general adoption as the symbol representing these two ratios. === ---- ===*Euler, Leonhard (1707-83), Swiss mathematician who was the most creative and

productive mathematician of the 18th century. His work exhibited a widespread use of

algebraic methods for treating problems in many different areas; it runs to 70 volumes

and includes essays on the tides, shipbuilding, and navigation, as well as on mainstreamtopics in pure and applied mathematics. Euler invented many mathematical notations

which are still employed today. He used e for the base of natural logarithms, i for (-1),

and f(x) for a function of x. ===