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PRESENTATION ON

HISTORY OF PI

2010-2011

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ST STEPHENES SENIOR SECANDRY SCHOOL

AJMER

PROJECTONMATHS

HISTORY OF PITOPIC:-

SUBMITTEDTO:- SIR ALOK

SUBMITTEDBY:- NITIN CHANDWANI

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INTRODUCTION TO PI

FACTS OF PI

PROOF

WHAT IS PI ?

DISCOVEREY OF PI

THE END

INDE

X

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The Greek letter pirepresents the number bywhich the diameter of acircle must be multipliedto obtain thecircumference. Pi is anirrational number. That is,itcannot be written as a

simple

INTRODUCTION TO PI

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fraction or as an exactdecimal with a finitenumber of decimalplaces. However, youcan increase thenumber of digits untilyou reach a number as

near to pi as needed.Mathematicians withcomputers havecalculated pito millions

of decimal places.

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Pi is used in severalmathematical

calculations. Thecircumference of acircle can be found bymultiplying the

adiameter by pi (c = pi Xd). The area of a circleis yielded by multiplyingpi by the radius

squared(A = pi X r-squared). Pi is alsoused to calculate

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the area of a circle,and the volume ofsphere or a cone

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The fact that the ratio ofthe circaumference tothe diameter of a circle

is constant has beenknown for so long that itis quite untraceable.The earliest values of including the 'Biblical'value of 3, were almostcertainly found

FACTS OF PI

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by measurement. In theEgyptian Rhind Papyrus,which is dated about 1650BC, there is good evidence

for 4 (8/9)2 = 3.16 as avalue for .

The first theoreticalcalculation seems to havebeen carried out byArchimedes ofSyracuse (287-212 BC). Heobtained the approximation

223/71 < < 22/7.

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Before giving anindication of his proof,notice that very

considerablesophistication involvedin the use of inequalitieshere. Archimedes knew,what so many people tothis day do not, that does not equal 22/7,and made

PROOF

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no claim to havediscovered the exactvalue. If we take hisbest estimate as theaverage of his twobounds we obtain3.1418, an error ofabout 0.0002.

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PI IS A GREEKLETERUSED INMATHEMATICS

IT IS SAME FOREVERY SIZE OF ACIRCLE

PI IS EQUALS TO 22/7

(PI)=22/7

WHAT IS PI ?

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THE FIRSTCALCULATION OF PIWAS TAKEN BY

ARCHIMEDE IN (287-

212BC)

HE OBTAINEDAPPROXIMATELY221/73

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PI/4 = 1- 1/3 + 1/5 - 1/7 + ....

THIS FORMULA ISSOMETIME

ATRIBUTED BYLEIBNIZ (1646-1761)BUT SEEMS IS SEEMSTO HAVE BEEN FIRSTDISCOVEREDBY JAMES GREGORY(1638-1675)

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SHANKS KNEW THATTHE PI WAS

IRATIONAL SINCETHIS HAD BEENPROVED IN 1761 BYLAMBERT

AFTER SHANKSCALCULATION IT WASSHOWN BYLINDEMANN THAT PI

IS TRANSCENDENTAL

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Europeanmathematicians in theearly modern perioddeveloped newarithmetical formulae toapproximate the valueof pi, such as that ofJames Gregory (1638-1675), which was takenup by Leibniz:

PI/4 = 1 - 1/3 +1/5 - 1/7 + . . .

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I THANK SIR ALOK FOR GIVING ME THISOPORTUNITY TO PREPARE A PROJECTON HISTORY OF PI.

THE END