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8/4/2019 Maths Project by Nitin Chandwani X-b 22
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PRESENTATION ON
HISTORY OF PI
2010-2011
X-B
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ST STEPHENES SENIOR SECANDRY SCHOOL
AJMER
PROJECTONMATHS
HISTORY OF PITOPIC:-
SUBMITTEDTO:- SIR ALOK
SUBMITTEDBY:- NITIN CHANDWANI
X-B
22
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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