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Calculation of Pi Using the Gregory-Leibniz Series |
Realtime-calculation with 1000 iterations:
4.0As you can see, this converges very slowly, with large, alternating over-estimates and under-estimates.
2.66666666667
3.46666666667
2.89523809524
3.33968253968
2.97604617605
3.28373848374
3.01707181707
3.25236593472
3.04183961893
3.23231580941
3.05840276593
3.21840276593
3.07025461778
3.20818565226
3.0791533942
3.20036551541
3.08607980113
3.19418790924
3.09162380667
3.18918478228
3.09616152647
3.18505041536
3.09994403238
3.18157668544
3.10314531289
3.178617011
3.10588973827
3.17606517687
3.1082685667
3.17384233719
3.1103502737
3.17188873524
3.1121872427
3.1701582572
3.11382022903
3.16861474958
3.11528141624
3.16722946819
3.1165965568
3.16597927285
3.11778650176
3.16484532529
3.1188683138
3.16381213402
3.11985609006
3.16286684275
3.1207615796
3.161998693
3.1215946526
3.16119861299
3.12236366154
3.16045889963
3.12307572206
3.15977296977
3.12373693373
3.15913516382
3.12435255512
3.15854058931
3.12492714393
3.15798499517
3.12546466997
3.15746466997
3.12596860698
3.15697635891
3.12644200777
3.15651719574
3.12688756611
3.1560846464
3.12730766798
3.15567646231
3.12770443434
3.15529064124
3.12807975688
3.15492539447
3.12843532824
3.15457911909
3.12877266748
3.15425037449
3.12909314178
3.15393786228
3.12939798498
3.15364040922
3.12968831342
3.15335695247
3.1299651396
3.15308652689
3.13022938403
3.15282825409
3.13048188537
3.15258133288
3.13072340939
3.15234503101
3.13095465668
3.15211867784
3.13117626946
3.15190165806
3.13138883755
3.15169340608
3.13159290357
3.15149340108
3.13178896758
3.1513011627
3.13197749121
3.15111624719
3.13215890122
3.15093824394
3.13233359278
3.1507667725
3.13250193232
3.15060147983
3.1326642601
3.15044203787
3.1328208925
3.1502881414
3.13297212409
3.15013950606
3.13311822947
3.1499958666
3.13325946493
3.1498569753
3.13339606995
3.14972260056
3.13352826858
3.14959252561
3.13365627063
3.14946654731
3.1337802728
3.14934447514
3.13390045969
3.14922613019
3.13401700472
3.14911134434
3.13413007093
3.14899995941
3.13423981181
3.14889182646
3.13434637192
3.14878680513
3.13444988756
3.14868476301
3.13455048739
3.14858557511
3.13464829288
3.14848912333
3.13474341886
3.14839529599
3.13483597396
3.14830398743
3.13492606101
3.14821509755
3.13501377742
3.14812853152
3.13509921556
3.14804419938
3.13518246304
3.14796201576
3.13526360306
3.14788189959
3.13534271464
3.14780377383
3.1354198729
3.14772756521
3.1354951493
3.14765320402
3.13556861187
3.14758062388
3.13564032538
3.14750976158
3.13571035155
3.14744055683
3.13577874925
3.14737295215
3.13584557463
3.14730689268
3.13591088128
3.14724232604
3.13597472041
3.1471792022
3.13603714092
3.14711747333
3.13609818958
3.14705709369
3.13615791113
3.14699801953
3.13621634837
3.14694020896
3.13627354229
3.14688362187
3.13632953216
3.14682821982
3.1363843556
3.14677396598
3.13643804867
3.14672082502
3.13649064599
3.14666876304
3.13654218076
3.14661774751
3.13659268486
3.1465677472
3.13664218889
3.1465187321
3.13669072227
3.14647067337
3.13673831327
3.1464235433
3.13678498908
3.14637731522
3.13683077584
3.14633196349
3.13687569871
3.14628746342
3.13691978192
3.14624379124
3.13696304878
3.14620092407
3.13700552177
3.14615883984
3.13704722253
3.14611751732
3.13708817194
3.14607693599
3.13712839013
3.1460370761
3.1371678965
3.14599791857
3.13720670978
3.14595944501
3.13724484806
3.14592163765
3.13728232879
3.14588447933
3.13731916884
3.14584795348
3.13735538448
3.1458120441
3.13739099147
3.1457767357
3.13742600502
3.14574201333
3.13746043983
3.14570786251
3.13749431015
3.14567426925
3.13752762974
3.14564122
3.13756041192
3.14560870166
3.1375926696
3.14557670154
3.13762441525
3.14554520733
3.13765566098
3.14551420715
3.1376864185
3.14548368946
3.13771669916
3.14545364307
3.13774651398
3.14542405716
3.13777587361
3.14539492123
3.1378047884
3.14536622507
3.13783326839
3.14533795882
3.1378613233
3.14531011288
3.1378889626
3.14528267794
3.13791619543
3.14525564497
3.13794303071
3.14522900521
3.13796947708
3.14520275014
3.13799554293
3.14517687147
3.13802123641
3.14515136118
3.13804656545
3.14512621146
3.13807153774
3.14510141472
3.13809616078
3.14507696357
3.13812044183
3.14505285084
3.13814438798
3.14502906956
3.1381680061
3.14500561293
3.13819130288
3.14498247436
3.13821428485
3.14495964741
3.13823695834
3.14493712584
3.13825932951
3.14491490356
3.13828140438
3.14489297463
3.1383031888
3.1448713333
3.13832468846
3.14484997394
3.1383459089
3.14482889107
3.13836685553
3.14480807936
3.13838753361
3.14478753361
3.13840794828
3.14476724876
3.13842810454
3.14474721987
3.13844800727
3.14472744212
3.13846766121
3.14470791082
3.13848707101
3.1446886214
3.13850624118
3.14466956938
3.13852517614
3.14465075041
3.13854388018
3.14463216024
3.13856235751
3.14461379472
3.13858061222
3.14459564981
3.13859864831
3.14457772156
3.13861646969
3.1445600061
3.13863408017
3.14454249967
3.13865148347
3.14452519859
3.13866868322
3.14450809928
3.13868568298
3.14449119822
3.1387024862
3.14447449198
3.13871909629
3.14445797721
3.13873551655
3.14444165065
3.13875175022
3.14442550908
3.13876780046
3.1444095494
3.13878367036
3.14439376853
3.13879936294
3.14437816349
3.13881488116
3.14436273136
3.13883022791
3.14434746929
3.13884540602
3.14433237446
3.13886041824
3.14431744416
3.13887526729
3.1443026757
3.13888995581
3.14428806647
3.13890448639
3.1442736139
3.13891886156
3.1442593155
3.13893308381
3.1442451688
3.13894715556
3.14423117141
3.13896107918
3.14421732097
3.13897485701
3.14420361518
3.13898849132
3.14419005178
3.13900198434
3.14417662858
3.13901533826
3.14416334341
3.13902855522
3.14415019414
3.13904163731
3.14413717871
3.13905458659
3.14412429508
3.13906740507
3.14411154126
3.13908009472
3.1440989153
3.13909265748
3.14408641528
3.13910509523
3.14407403933
3.13911740984
3.14406178561
3.13912960312
3.14404965232
3.13914167686
3.14403763769
3.13915363281
3.14402574
3.13916547268
3.14401395753
3.13917719816
3.14400228863
3.13918881089
3.14399073166
3.1392003125
3.14397928502
3.13921170457
3.14396794714
3.13922298866
3.14395671647
3.13923416629
3.1439455915
3.13924523897
3.14393457074
3.13925620817
3.14392365275
3.13926707533
3.14391283608
3.13927784187
3.14390211932
3.13928850918
3.14389150112
3.13929907862
3.1438809801
3.13930955153
3.14387055495
3.13931992924
3.14386022436
3.13933021304
3.14384998705
3.13934040418
3.14383984176
3.13935050393
3.14382978725
3.1393605135
3.14381982231
3.1393704341
3.14380994576
3.13938026691
3.14380015641
3.13939001308
3.14379045313
3.13939967376
3.14378083477
3.13940925007
3.14377130024
3.13941874311
3.14376184843
3.13942815395
3.14375247828
3.13943748367
3.14374318873
3.1394467333
3.14373397875
3.13945590388
3.14372484732
3.13946499641
3.14371579344
3.13947401189
3.14370681612
3.13948295128
3.1436979144
3.13949181556
3.14368908733
3.13950060566
3.14368033397
3.1395093225
3.1436716534
3.13951796701
3.14366304473
3.13952654008
3.14365450705
3.13953504258
3.1436460395
3.1395434754
3.14363764121
3.13955183937
3.14362931134
3.13956013534
3.14362104905
3.13956836414
3.14361285353
3.13957652658
3.14360472396
3.13958462346
3.14359665957
3.13959265556
3.14358865956
3.13960062367
3.14358072317
3.13960852854
3.14357284965
3.13961637092
3.14356503824
3.13962415154
3.14355728822
3.13963187114
3.14354959886
3.13963953043
3.14354196945
3.13964713012
3.14353439931
3.13965467089
3.14352688773
3.13966215343
3.14351943405
3.13966957842
3.14351203759
3.1396769465
3.1435046977
3.13968425835
3.14349741374
3.13969151459
3.14349018506
3.13969871586
3.14348301104
3.13970586278
3.14347589106
3.13971295597
3.14346882452
3.13971999602
3.1434618108
3.13972698354
3.14345484934
3.1397339191
3.14344793953
3.1397408033
3.14344108082
3.13974763668
3.14343427262
3.13975441982
3.1434275144
3.13976115327
3.1434208056
3.13976783756
3.14341414568
3.13977447325
3.1434075341
3.13978106084
3.14340097035
3.13978760088
3.1433944539
3.13979409386
3.14338798425
3.1398005403
3.1433815609
3.1398069407
3.14337518334
3.13981329554
3.1433688511
3.13981960531
3.14336256368
3.13982587049
3.14335632062
3.13983209155
3.14335012145
3.13983826895
3.1433439657
3.13984440315
3.14333785293
3.1398504946
3.14333178268
3.13985654375
3.14332575451
3.13986255104
3.14331976798
3.1398685169
3.14331382268
3.13987444176
3.14330791816
3.13988032604
3.14330205402
3.13988617016
3.14329622983
3.13989197451
3.1432904452
3.13989773952
3.14328469972
3.13990346557
3.143278993
3.13990915306
3.14327332464
3.13991480238
3.14326769425
3.13992041392
3.14326210147
3.13992598804
3.14325654591
3.13993152513
3.1432510272
3.13993702555
3.14324554498
3.13994248966
3.14324009889
3.13994791782
3.14323468857
3.13995331039
3.14322931366
3.13995866771
3.14322397384
3.13996399014
3.14321866874
3.139969278
3.14321339803
3.13997453163
3.14320816138
3.13997975137
3.14320295846
3.13998493755
3.14319778895
3.13999009048
3.14319265252
3.13999521048
3.14318754886
3.14000029787
3.14318247766
3.14000535296
3.1431774386
3.14001037606
3.14317243139
3.14001536746
3.14316745572
3.14002032748
3.14316251129
3.14002525639
3.14315759782
3.1400301545
3.143152715
3.14003502209
3.14314786256
3.14003985945
3.14314304021
3.14004466686
3.14313824768
3.14004944459
3.14313348468
3.14005419292
3.14312875095
3.14005891212
3.14312404622
3.14006360246
3.14311937022
3.14006826419
3.14311472268
3.14007289759
3.14311010336
3.1400775029
3.14310551199
3.14008208039
3.14310094832
3.1400866303
3.1430964121
3.14009115289
3.14309190308
3.1400956484
3.14308742102
3.14010011706
3.14308296568
3.14010455913
3.14307853683
3.14010897484
3.14307413422
3.14011336442
3.14306975762
3.1401177281
3.1430654068
3.14012206611
3.14306108154
3.14012637868
3.14305678161
3.14013066603
3.14305250679
3.14013492838
3.14304825686
3.14013916595
3.1430440316
3.14014337895
3.1430398308
3.1401475676
3.14303565424
3.14015173211
3.14303150173
3.14015587268
3.14302737304
3.14015998953
3.14302326798
3.14016408285
3.14301918635
3.14016815285
3.14301512794
3.14017219972
3.14301109255
3.14017622366
3.14300708
3.14018022488
3.14300309008
3.14018420354
3.14299912262
3.14018815986
3.1429951774
3.14019209401
3.14299125426
3.14019600618
3.14298735301
3.14019989656
3.14298347346
3.14020376533
3.14297961543
3.14020761266
3.14297577875
3.14021143874
3.14297196324
3.14021524373
3.14296816872
3.14021902782
3.14296439502
3.14022279118
3.14296064196
3.14022653397
3.1429569094
3.14023025636
3.14295319714
3.14023395853
3.14294950503
3.14023764062
3.1429458329
3.14024130282
3.1429421806
3.14024494527
3.14293854796
3.14024856814
3.14293493482
3.14025217158
3.14293134103
3.14025575575
3.14292776644
3.1402593208
3.14292421088
3.1402628669
3.1429206742
3.14026639418
3.14291715627
3.1402699028
3.14291365693
3.1402733929
3.14291017602
3.14027686464
3.14290671342
3.14028031815
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3.14028375358
3.14289984253
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3.14289643396
3.14029057076
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3.14029395279
3.14288966986
3.1402973173
3.14288631406
3.14030066442
3.14288297559
3.14030399428
3.1428796543
3.14030730703
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3.14031060279
3.14287306275
3.14031388168
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3.14031714386
3.14286653838
3.14032038943
3.14286330106
3.14032361852
3.14286008016
3.14032683126
3.14285687554
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3.14033637263
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3.1403395212
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3.1428410925
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3.14034887293
3.14283488909
3.14035195923
3.14283181044
3.14035503026
3.14282874702
3.14035808612
3.1428256987
3.14036112692
3.14282266538
3.14036415278
3.14281964695
3.14036716381
3.14281664329
3.14037016011
3.14281365431
3.1403731418
3.14281067989
3.14037610898
3.14280771992
3.14037906176
3.14280477431
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3.1403907309
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3.14278739625
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3.1427595143
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3.14275679751
3.14042986324
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3.14043256113
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3.14043524653
3.14274872252
3.14043791952
3.1427460557
3.1404405802
3.14274340115
3.14044322864
3.1427407588
3.14044586494
3.14273812855
3.14044848917
3.14273551032
3.14045110142
3.14273290404
3.14045370176
3.14273030962
3.14045629029
3.14272772697
3.14045886708
3.14272515603
3.1404614322
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3.14271751259
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3.14047157767
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3.14270997164
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3.14047906815
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3.14048154278
3.14270253112
3.14048400644
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3.14048890113
3.14269518905
3.1404913323
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3.14050569736
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3.14052199005
3.14266217196
3.14052427779
3.14265988911
3.14052655578
3.14265761598
3.14052882407
3.14265535251
3.14053108273
3.14265309864
3.14053333182
3.14265085432
3.1405355714
3.14264861947
3.14053780153
3.14264639405
3.14054002227
3.14264417798
3.14054223368
3.14264197121
3.14054443582
3.14263977369
3.14054662874
3.14263758535
3.1405488125
3.14263540614
3.14055098717
3.142633236
3.1405531528
3.14263107487
3.14055530943
3.1426289227
3.14055745714
3.14262677944
3.14055959598
3.14262464502
3.14056172599
3.14262251939
3.14056384724
3.1426204025
3.14056595977
3.1426182943
3.14056806365
3.14261619473
3.14057015893
3.14261410374
3.14057224565
3.14261202127
3.14057432387
3.14260994728
3.14057639364
3.14260788171
3.14057845502
3.14260582451
3.14058050805
3.14260377563
3.14058255279
3.14260173502
3.14058458928
3.14259970263
3.14058661758
3.14259767842
3.14058863773
3.14259566232
3.14059064979
3.1425936543
3.1405926538
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pi
I love pi, its the coolest number!
-- Douglas Abbott
Pi
Pi is so cool! It is my favorite number, and I have a website with pi.
-- Nick Markenson
Pi-ism
We believe in Pi. Check us out at www.pisonearth.com
-- Pi-ism Belief Society
Website
Sorry, but the website got shut down.
-- Nick Markenson
Mathworld
Just want to lead your interest to the MAthworld site. There's a bunch of facts and describtions - among others. http://mathworld.wolfram.com/GregorySeries.html:-)
-- Claus Eriksen
I built a program that uses the Gregory-Leibniz method just moments after reading this. I have run my program for a little over 10 min. and on the 11,458,894'th iteration, I got 3.141592566. The program goes though about 10000 iterations a second, but still takes a long time to generate the digits. The first 5 come instantly, but after that it takes a while...
Attachment: pi-Gregory-Leibniz.exe
-- Aaron Gutierrez
