The First 10,000 digits of Pi
Of course, who needs to use the formula when you have about the first 10,000 digits right here!
3.1415926535897932384626433832795028841971693993751058209749445923078164062862
089986280348253421170679821480865132823066470938446095505822317253594081284811
174502841027019385211055596446229489549303819644288109756659334461284756482337
867831652712019091456485669234603486104543266482133936072602491412737245870066
063155881748815209209628292540917153643678925903600113305305488204665213841469
519415116094330572703657595919530921861173819326117931051185480744623799627495
673518857527248912279381830119491298336733624406566430860213949463952247371907
021798609437027705392171762931767523846748184676694051320005681271452635608277
857713427577896091736371787214684409012249534301465495853710507922796892589235
420199561121290219608640344181598136297747713099605187072113499999983729780499
510597317328160963185950244594553469083026425223082533446850352619311881710100
031378387528865875332083814206171776691473035982534904287554687311595628638823
537875937519577818577805321712268066130019278766111959092164201989380952572010
654858632788659361533818279682303019520353018529689957736225994138912497217752
834791315155748572424541506959508295331168617278558890750983817546374649393192
550604009277016711390098488240128583616035637076601047101819429555961989467678
374494482553797747268471040475346462080466842590694912933136770289891521047521
620569660240580381501935112533824300355876402474964732639141992726042699227967
823547816360093417216412199245863150302861829745557067498385054945885869269956
909272107975093029553211653449872027559602364806654991198818347977535663698074
265425278625518184175746728909777727938000816470600161452491921732172147723501
414419735685481613611573525521334757418494684385233239073941433345477624168625
189835694855620992192221842725502542568876717904946016534668049886272327917860
857843838279679766814541009538837863609506800642251252051173929848960841284886
269456042419652850222106611863067442786220391949450471237137869609563643719172
874677646575739624138908658326459958133904780275900994657640789512694683983525
957098258226205224894077267194782684826014769909026401363944374553050682034962
524517493996514314298091906592509372216964615157098583874105978859597729754989
301617539284681382686838689427741559918559252459539594310499725246808459872736
446958486538367362226260991246080512438843904512441365497627807977156914359977
001296160894416948685558484063534220722258284886481584560285060168427394522674
676788952521385225499546667278239864565961163548862305774564980355936345681743
241125150760694794510965960940252288797108931456691368672287489405601015033086
179286809208747609178249385890097149096759852613655497818931297848216829989487
226588048575640142704775551323796414515237462343645428584447952658678210511413
547357395231134271661021359695362314429524849371871101457654035902799344037420
073105785390621983874478084784896833214457138687519435064302184531910484810053
706146806749192781911979399520614196634287544406437451237181921799983910159195
618146751426912397489409071864942319615679452080951465502252316038819301420937
621378559566389377870830390697920773467221825625996615014215030680384477345492
026054146659252014974428507325186660021324340881907104863317346496514539057962
685610055081066587969981635747363840525714591028970641401109712062804390397595
156771577004203378699360072305587631763594218731251471205329281918261861258673
215791984148488291644706095752706957220917567116722910981690915280173506712748
583222871835209353965725121083579151369882091444210067510334671103141267111369
908658516398315019701651511685171437657618351556508849099898599823873455283316
355076479185358932261854896321329330898570642046752590709154814165498594616371
802709819943099244889575712828905923233260972997120844335732654893823911932597
463667305836041428138830320382490375898524374417029132765618093773444030707469
211201913020330380197621101100449293215160842444859637669838952286847831235526
582131449576857262433441893039686426243410773226978028073189154411010446823252
716201052652272111660396665573092547110557853763466820653109896526918620564769
312570586356620185581007293606598764861179104533488503461136576867532494416680
396265797877185560845529654126654085306143444318586769751456614068007002378776
591344017127494704205622305389945613140711270004078547332699390814546646458807
972708266830634328587856983052358089330657574067954571637752542021149557615814
002501262285941302164715509792592309907965473761255176567513575178296664547791
745011299614890304639947132962107340437518957359614589019389713111790429782856
475032031986915140287080859904801094121472213179476477726224142548545403321571
853061422881375850430633217518297986622371721591607716692547487389866549494501
146540628433663937900397692656721463853067360965712091807638327166416274888800
786925602902284721040317211860820419000422966171196377921337575114959501566049
631862947265473642523081770367515906735023507283540567040386743513622224771589
150495309844489333096340878076932599397805419341447377441842631298608099888687
413260472156951623965864573021631598193195167353812974167729478672422924654366
800980676928238280689964004824354037014163149658979409243237896907069779422362
508221688957383798623001593776471651228935786015881617557829735233446042815126
272037343146531977774160319906655418763979293344195215413418994854447345673831
624993419131814809277771038638773431772075456545322077709212019051660962804909
263601975988281613323166636528619326686336062735676303544776280350450777235547
105859548702790814356240145171806246436267945612753181340783303362542327839449
753824372058353114771199260638133467768796959703098339130771098704085913374641
442822772634659470474587847787201927715280731767907707157213444730605700733492
436931138350493163128404251219256517980694113528013147013047816437885185290928
545201165839341965621349143415956258658655705526904965209858033850722426482939
728584783163057777560688876446248246857926039535277348030480290058760758251047
470916439613626760449256274204208320856611906254543372131535958450687724602901
618766795240616342522577195429162991930645537799140373404328752628889639958794
757291746426357455254079091451357111369410911939325191076020825202618798531887
705842972591677813149699009019211697173727847684726860849003377024242916513005
005168323364350389517029893922334517220138128069650117844087451960121228599371
623130171144484640903890644954440061986907548516026327505298349187407866808818
338510228334508504860825039302133219715518430635455007668282949304137765527939
751754613953984683393638304746119966538581538420568533862186725233402830871123
282789212507712629463229563989898935821167456270102183564622013496715188190973
038119800497340723961036854066431939509790190699639552453005450580685501956730
229219139339185680344903982059551002263535361920419947455385938102343955449597
783779023742161727111723643435439478221818528624085140066604433258885698670543
154706965747458550332323342107301545940516553790686627333799585115625784322988
273723198987571415957811196358330059408730681216028764962867446047746491599505
497374256269010490377819868359381465741268049256487985561453723478673303904688
383436346553794986419270563872931748723320837601123029911367938627089438799362
016295154133714248928307220126901475466847653576164773794675200490757155527819
653621323926406160136358155907422020203187277605277219005561484255518792530343
513984425322341576233610642506390497500865627109535919465897514131034822769306
247435363256916078154781811528436679570611086153315044521274739245449454236828
860613408414863776700961207151249140430272538607648236341433462351897576645216
413767969031495019108575984423919862916421939949072362346468441173940326591840
443780513338945257423995082965912285085558215725031071257012668302402929525220
118726767562204154205161841634847565169998116141010029960783869092916030288400
269104140792886215078424516709087000699282120660418371806535567252532567532861
291042487761825829765157959847035622262934860034158722980534989650226291748788
202734209222245339856264766914905562842503912757710284027998066365825488926488
025456610172967026640765590429099456815065265305371829412703369313785178609040
708667114965583434347693385781711386455873678123014587687126603489139095620099
393610310291616152881384379099042317473363948045759314931405297634757481193567
091101377517210080315590248530906692037671922033229094334676851422144773793937
517034436619910403375111735471918550464490263655128162288244625759163330391072
253837421821408835086573917715096828874782656995995744906617583441375223970968
340800535598491754173818839994469748676265516582765848358845314277568790029095
170283529716344562129640435231176006651012412006597558512761785838292041974844
236080071930457618932349229279650198751872127267507981255470958904556357921221
033346697499235630254947802490114195212382815309114079073860251522742995818072
471625916685451333123948049470791191532673430282441860414263639548000448002670
496248201792896476697583183271314251702969234889627668440323260927524960357996
469256504936818360900323809293459588970695365349406034021665443755890045632882
250545255640564482465151875471196218443965825337543885690941130315095261793780
029741207665147939425902989695946995565761218656196733786236256125216320862869
222103274889218654364802296780705765615144632046927906821207388377814233562823
608963208068222468012248261177185896381409183903673672220888321513755600372798
394004152970028783076670944474560134556417254370906979396122571429894671543578
468788614445812314593571984922528471605049221242470141214780573455105008019086
996033027634787081081754501193071412233908663938339529425786905076431006383519
834389341596131854347546495569781038293097164651438407007073604112373599843452
251610507027056235266012764848308407611830130527932054274628654036036745328651
057065874882256981579367897669742205750596834408697350201410206723585020072452
256326513410559240190274216248439140359989535394590944070469120914093870012645
600162374288021092764579310657922955249887275846101264836999892256959688159205
60010165525637568
Everyone could use the table of computation of Pi!!!
Babylonians 2000? BCE 1 3.125 = 3 + 1/8 Egyptians 2000? BCE 1 3.16045 China 1200? BCE 1 3 Bible (1 Kings 7:23) 550? BCE 1 3 Archimedes 250? BCE 3 3.1418 (ave.) Hon Han Shu 130 AD 1 3.1622 = sqrt(10) ? Ptolemy 150 3 3.14166 Chung Hing 250? 1 3.16227 = sqrt(10) Wang Fau 250? 1 3.15555 = 142/45 Liu Hui 263 5 3.14159 Siddhanta 380 3 3.1416 Tsu Ch'ung Chi 480? 7 3.1415926 Aryabhata 499 4 3.14156 Brahmagupta 640? 1 3.162277 = sqrt(10) AlKhowarizmi 800 4 3.1416 Fibonacci 1220 3 3.141818 AlKashi 1429 14 Otho 1573 6 3.1415929 Viete 1593 9 3.1415926536 (ave.) Romanus 1593 15 Van Ceulen 1596 20 Van Ceulen 1615 35 Newton 1665 16 Sharp 1699 71 Seki 1700? 10 Kamata 1730? 25 Machin 1706 100 De Lagny 1719 127 (112 correct) Takebe 1723 41 Matsunaga 1739 50 Vega 1794 140 Rutherford 1824 208 (152 correct) Strassnitzky and Dase 1844 200 Clausen 1847 248 Lehmann 1853 261 Rutherford 1853 440 Shanks 1874 707 (527 correct)
Ferguson 1946 620 Ferguson Jan. 1947 710 Ferguson and Wrench Sep. 1947 808 Smith and Wrench 1949 1,120 Reitwiesner et al. (ENIAC) 1949 2,037 Nicholson and Jeenel 1954 3,092 Felton 1957 7,480 Genuys Jan. 1958 10,000 Felton May 1958 10,021 Guilloud 1959 16,167 Shanks and Wrench 1961 100,265 Guilloud and Filliatre 1966 250,000 Guilloud and Dichampt 1967 500,000 Guilloud and Bouyer 1973 1,001,250 Miyoshi and Kanada 1981 2,000,036 Guilloud 1982 2,000,050 Tamura 1982 2,097,144 Tamura and Kanada 1982 4,194,288 Tamura and Kanada 1982 8,388,576 Kanada, Yoshino and Tamura 1982 16,777,206 Ushiro and Kanada Oct. 1983 10,013,395 Gosper 1985 17,526,200 Bailey Jan. 1986 29,360,111 Kanada and Tamura Sep. 1986 33,554,414 Kanada and Tamura Oct. 1986 67,108,839 Kanada, Tamura, Kubo et al Jan. 1987 134,217,700 Kanada and Tamura Jan. 1988 201,326,551 Chudnovskys May 1989 480,000,000 Chudnovskys Jun. 1989 525,229,270 Kanada and Tamura Jul. 1989 536,870,898 Kanada and Tamura Nov. 1989 1,073,741,799 Chudnovskys Aug. 1989 1,011,196,691 Chudnovskys Aug. 1991 2,260,000,000 Chudnovskys May 1994 4,044,000,000 Takahashi and Kanada Jun. 1995 3,221,225,466 Takahashi and Kanada Aug. 1995 4,294,967,286 Takahashi and Kanada Oct. 1995 6,442,450,938
Bailey, Borwein, Plouffe Nov. 1995 40,000,000,000 (hexa 921C73C6838FB2) Bellard Jul. 1996 200,000,000,000 (hexa 1A10A49B3E2B82A4404F9193AD4EB6) Bellard Oct. 1996 400,000,000,000 (hexa 9C381872D27596F81D0E48B95A6C46)
Pi Facts
I bet you don't know this much about pi!
p = 4 x (Area of
circle) / (Area of square)
11.0010010000111111011010101000100010000101101000110000100011010011
You
can do lots more stuff with Pi when it is in binary format  like drawing weird
pictures of it, or even listening to it. As Pi has an infinite number of places,
it is quite possible that any message you liked could be heard somewhere in Pi.
It has even been suggested it contains the VOICE OF GOD. In Carl Sagan's book
'Contact' the places of Pi (in base 11) are found to contain a message from the
beings that built the universe
0 occurs 599963005 times
1 occurs 600033260 times
2 occurs 599999169 times
3 occurs 600000243 times
4 occurs 599957439 times
5 occurs 600017176 times
6 occurs 600016588 times
7 occurs 600009044 times
8 occurs 599987038 times
9 occurs 600017038 times
This shows NO unusual deviation
from expected 'random' behavior
Then
the circle's circumference is twice the base length of the pyramid, and the
circle's area is equal to the pyramid's vertical sectional area through the
peak. The ratio of the perimeter of the base of the Great Pyramid to its height
is twice Pi. The same ratio for the Pyramid of the Sun in Mexico is four times
Pi. Both are built to an accuracy of a few inches.
And
he made a molten sea, ten cubits from one brim to the other: it was round all
about, and his height was five cubits: and a line of thirty cubits did compass
it about
Wallis: p = (8 / 3) .
(4.4.6.6.8.8.10.10.12...) / (3.5.5.7.7.9.9.11.11...)
This
is very slow to converge  After 7000 terms it is accurate to 7 decimal places
(averaging terms 7000 and 7001)
Gregory (also attributed to Leibniz):
p = 4  (4/3) + (4/5)  (4/7) + (4/9)  (4/11) + ...
This is about the same  After 7000
terms it is also accurate to 7 decimal places
p = Sqrt ( 12 
(12/2^{2}) + (12/3^{2})  (12/4^{2}) + ...
This is slightly faster  After
just 1100 terms it is accurate to at least 9 decimal places
There are many other such formulas
·
Ramanujan developed a formula for Pi which adds 8 decimal places
each term!
This is the formula generally used
by supercomputers to calculate Pi
·
David Bailey, Peter Borwein and Simon Plouffe recently computed
the ten billionth digit in the hexadecimal expansion of Pi. They used an
astonishing formula:
which
enables one to calculate the nth digit of Pi without being forced to calculate
all the preceding n 1 digits. No one had previously even conjectured that such
a digitextraction algorithm for Pi was possible
10^{1/2 }
Cube root of 31
^{666}/_{212 }
^{10}/p
(97 + ^{9}/_{22})^{1/4 }
^{9}/_{5} + (^{9}/_{5})^{1/2 }
(19 (7)^{1/2}) / 16
(2)^{1/2} + (3)^{1/2}
1.1 x 1.2 x 1.4 x 1.7
(^{296}/_{167})^{ 2 }
p + e
p /e
lnp
Three point one four one five nine
two
Its been around forever  it's not
new
It appears everywhere
In here and in there
Its irrational I know but its true!
Simmy's Pages  

Pi We have known about pi for four millenniums, calculated millions of its digits, and even created a holiday just for it. It is used everyday by students and highly skilled math theorists alike. Because it is one of the most important numbers in the world, we decided it should have at least its own webpage. Calculating Pi There is a fairly simple formula you can use if you want
to calculate pi. so that would simplify out to 4[Arc Tangent(1)] = Pi
