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Questions about Pi


Date: 12/5/95 at 9:43:29
From: Anonymous
Subject: Pi

Why does pi repeat so much and can you write it out for me?


Date: 12/14/95 at 22:45:6
From: Doctor Ken
Subject: Re: Pi

Hello!

Actually, it's not quite right to say that Pi "repeats," since that has 
a precise meaning in math: it means that if you look at the digits after 
the decimal point, there's a chunk of them that just gets repeated over 
and over forever.  In fact, Pi never ends up repeating the same chunk 
over and over, which is pretty cool.  It's an infinite decimal all right 
(you'll never get to its end), but it doesn't repeat the way 
5.2533333333... and 19.1234567567567567567567567... do.  

The difference between these two types of numbers is that the kind that
repeats is called "rational" - it can be written as a fraction, a 
ratio.  The kind that doesn't repeat, like Pi or the square root of 2, is 
called "irrational."  You can actually prove that those numbers can't be 
written as a fraction.

Here are the first few digits of Pi:

3.141592653589793238462643383279502884197169399375105820974944
592307816406286208998628034825342117067982148086513282306647
093844609550582231725359408128481117450284102701938521105559
644622948954930381964428810975665933446128475648233786783165
271201909145648566923460348610454326648213393607260249141273
724587006606315588174881520920962829254091715364367892590360
011330530548820466521384146951941511609433057270365759591953
092186117381932611793105118548074462379962749567351885752724
891227938183011949129833673362440656643086021394946395224737
190702179860943702770539217176293176752384674818467669405132
000568127145263560827785771342757789609173637178721468440901
224953430146549585371050792279689258923542019956112129021960
864034418159813629774771309960518707211349999998372978049951
059731732816096318595024459455346908302642522308253344685035
261931188171010003137838752886587533208381420617177669147303
598253490428755468731159562863882353787593751957781857780532
171226806613001927876611195909216420198938095257201065485863
278865936153381827968230301952035301852968995773622599413891
249721775283479131515574857242454150695950829533116861727855
889075098381754637464939319255060400927701671139009848824012
858361603563707660104710181942955596198946767837449448255379
774726847104047534646208046684259069491293313677028989152104
752162056966024058038150193511253382430035587640247496473263
914199272604269922796782354781636009341721641219924586315030
286182974555706749838505494588586926995690927210797509302955
321165344987202755960236480665499119881834797753566369807426
542527862551818417574672890977772793800081647060016145249192
173217214772350141441973568548161361157352552133475741849468
438523323907394143334547762416862518983569485562099219222184
272550254256887671790494601653466804988627232791786085784383
827967976681454100953883786360950680064225125205117392984896
084128488626945604241965285022210661186306744278622039194945
047123713786960956364371917287467764657573962413890865832645
995813390478027590099465764078951269468398352595709825822620
522489407726719478268482601476990902640136394437455305068203
496252451749399651431429809190659250937221696461515709858387
410597885959772975498930161753928468138268683868942774155991
855925245953959431049972524680845987273644695848653836736222
626099124608051243884390451244136549762780797715691435997700
129616089441694868555848406353422072225828488648158456028506
016842739452267467678895252138522549954666727823986456596116
354886230577456498035593634568174324112515076069479451096596
094025228879710893145669136867228748940560101503308617928680
920874760917824938589009714909675985261365549781893129784821
682998948722658804857564014270477555132379641451523746234364
542858444795265867821051141354735739523113427166102135969536
231442952484937187110145765403590279934403742007310578539062
198387447808478489683321445713868751943506430218453191048481
005370614680674919278191197939952061419663428754440643745123
718192179998391015919561814675142691239748940907186494231961
567945208095146550225231603881930142093762137855956638937787
....

Pretty neat, huh?

- Doctor Ken,  The Geometry Forum

    
Associated Topics:
Middle School Pi

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