A Piece Of Pi
Pi, which is denoted by the Greek letter (), is the most
famous ratio in mathematics, and is one of the
most ancient numbers known to humanity. PI is approximately 3.14, by definition,
the number of times that a circle's diameter will
fit around the circle. PI goes on forever, and
can't be calculated to perfect precision.
3.1415926535897932384626433832795028841971693993751....
On our site and in all of our calculators, 3.14159
is the value we use, unless otherwise specified.
(You can also calculate it yourself using our
PI Calculator. Dividing the PI(e)
has always been a problem but sometimes multiplying
with it is also. You can do either here; PI power is also available.) The
only exception is the expatiated calculation below.
(I didn't have much to do last night and TV was
terrible - the only thing on was the 8,534,565th
repeat of Hawaii 50 (divided by PI), so I calculated
PI to 10,000 places on my 1959, still working,
easy on the eye yellow, NASA issue, Pickett slide rule. I was going to try
for a million but the slide was a little dirty
and I felt accuracy MIGHT be compromised... We
certainly don't want to compromise PI!) The value
3.14159 was defined in 1998 by the Alabama legislature
as the official state value for PI. (I'll bet
you didn't know that you needed a state value
for PI. Of course, they also said that PI are
round and cornbread are squared... They would
have been better served to say that PI was to
personal taste.) This infinite calculation phenomena
is known as the decimal expansion of PI. No apparent
pattern emerges in the extreme succession of digits;
a predestined yet unfathomable code. They do not
repeat periodically, but seemingly do pop up repeating
a few sequences by blind chance, (lacking any
perceivable order, rule, reason, or design). In
1991, the Chudnovsky brothers in New York, using
their computer, m zero (in my opinion,
named for the important work it did), calculated
PI to two billion two hundred sixty million three
hundred twenty one thousand three hundred sixty
three digits (2,260,321,363). They halted the
program that summer. Was it important? Some thought
it was; others feel it was a waste of time, effort
and energy. PI has had various names (some of
them not fit for family viewing) through the ages,
and all of them are either words or abstract symbols
(something like the symbol for the entertainer
(?) formerly known as Prince...), since PI is
a number that can't be shown completely and exactly
in any finite form of reasonable representation.
PI is a true transcendental number, one that can't
be expressed in any finite series of either arithmetical
or algebraic operations. PI departs from all rational
methods to locate it. It is virtually indescribable
and can't be found. Ferdinand Lindemann, a German
mathematician, proved the transcendence of PI
in 1882, not that I felt he needed to prove it.
PI possibly first entered human consciousness
in Egypt. The earliest known reference to PI occurs
in a Middle Kingdom papyrus scroll (produced on
a very old MAC, or a bad Apple), written around
1650 BC by a scribe named Ahmes. He began the
scroll with the words, "The Entrance Into the
Knowledge of All Existing Things" and remarks
in passing that he composed the scroll "in likeness
to writings made of old." Towards the end of the
scroll, which is composed of various mathematical
problems and their solutions, the area of a circle
is found using a rough sort of PI. The next indication
of the value of PI occurs in the Bible. It is
found in 1 Kings chapter 7 verse 23, where using
the Authorized Version, it is written "... and
he made a molten sea, ten cubits from one brim
to the other: it was round about ... and a line
of thirty cubits did compass it round about."
Thus their value of PI was approximately 3. (Works
for me... I'm a believer!) Even though this is
not as accurate as values obtained by the Egyptians,
Babylonians and Indians, it was good enough for
measurements needed at that time, give or take
a cubit. Around 250 BC, Archimedes of Syracuse
found that PI is somewhere about 3.14 (in fractions,
Greeks did not yet have decimals in a math system).
Rumor has it, that is also when swearing started.
As time went on, other people were able come up
with better approximations (as opposed to calculations)
for PI. About 150 AD, Ptolemy of Alexandria (Egypt)
gave its value as 377/120 and in about 500 AD
the Chinese Tsu Ch'ung-Chi produced the value
as 355/113. These are correct to 3 and 6 decimal
places respectively. In fact, they are accurate
enough that MOST 8 place calculators of modern
era use one or the other as a basis for PI. (We
use the latter.) Knowledge of PI then bogged down
until the 17th century, shortly before Mr. Gates
introduced double precision numeric variables
in MBASIC (well it SEEMS like that long ago...).
PI was then called the Ludolphian number, after
Ludolph van Ceulen, a German mathematician. It
is also rumored that his number is used in the
price formula of BMWs. The first person to use
the Greek letter
for the number was William Jones (try keeping
up with him...), an English mathematician, who
coined it in 1706. Physicists have noted the ubiquity
of PI in nature. PI is obvious in the disks of
the moon and the sun. The double helix of DNA
revolves around PI. PI hides in the rainbow (and
in the refrigerator), and sits in the pupil of
the eye, and when a raindrop falls into water
PI emerges in the spreading rings. PI can be found
in waves and ripples and spectra of all kinds,
and therefore PI occurs in colors and music (and
sometimes at your local ATM or local Girl Scout
bake sales). PI has lately turned up in values
known as superstrings. PI occurs naturally in
tables of death, in what is known as a Gaussian
distribution of deaths in a population; that is,
when a person dies, the event "impacts" PI. It
is one of the great mysteries in life how nature
seems to know (of) mathematics; yet, for those
of us that are believers, it is really no mystery
at all. (Another great mystery of PI(e) is why
you can always find apple and cherry but seldom
egg custard.) Please see our Historical Computation Of PI Table.
(Source: The New
Yorkermagazine, March 2, 1992, called "Profiles: The
Mountains of PI")
|
PI To 10,000 Digits
1415926535 8979323846 2643383279
5028841971 6939937510 5820974944 5923078164 0628620899
8628034825 3421170679 8214808651 3282306647 0938446095
5058223172 5359408128 4811174502 8410270193 8521105559
6446229489 5493038196 4428810975 6659334461 2847564823
3786783165 2712019091 4564856692 3460348610 4543266482
1339360726 0249141273 7245870066 0631558817 4881520920
9628292540 9171536436 7892590360 0113305305 4882046652
1384146951 9415116094 3305727036 5759591953 0921861173
8193261179 3105118548 0744623799 6274956735 1885752724
8912279381 8301194912 9833673362 4406566430 8602139494
6395224737 1907021798 6094370277 0539217176 2931767523
8467481846 7669405132 0005681271 4526356082 7785771342
7577896091 7363717872 1468440901 2249534301 4654958537
1050792279 6892589235 4201995611 2129021960 8640344181
5981362977 4771309960 5187072113 4999999837 2978049951
0597317328 1609631859 5024459455 3469083026 4252230825
3344685035 2619311881 7101000313 7838752886 5875332083
8142061717 7669147303 5982534904 2875546873 1159562863
8823537875 9375195778 1857780532 1712268066 1300192787
6611195909 2164201989 3809525720 1065485863 2788659361
5338182796 8230301952 0353018529 6899577362 2599413891
2497217752 8347913151 5574857242 4541506959 5082953311
6861727855 8890750983 8175463746 4939319255 0604009277
0167113900 9848824012 8583616035 6370766010 4710181942
9555961989 4676783744 9448255379 7747268471 0404753464
6208046684 2590694912 9331367702 8989152104 7521620569
6602405803 8150193511 2533824300 3558764024 7496473263
9141992726 0426992279 6782354781 6360093417 2164121992
4586315030 2861829745 5570674983 8505494588 5869269956
9092721079 7509302955 3211653449 8720275596 0236480665
4991198818 3479775356 6369807426 5425278625 5181841757
4672890977 7727938000 8164706001 6145249192 1732172147
7235014144 1973568548 1613611573 5255213347 5741849468
4385233239 0739414333 4547762416 8625189835 6948556209
9219222184 2725502542 5688767179 0494601653 4668049886
2723279178 6085784383 8279679766 8145410095 3883786360
9506800642 2512520511 7392984896 0841284886 2694560424
1965285022 2106611863 0674427862 2039194945 0471237137
8696095636 4371917287 4677646575 7396241389 0865832645
9958133904 7802759009 9465764078 9512694683 9835259570
9825822620 5224894077 2671947826 8482601476 9909026401
3639443745 5305068203 4962524517 4939965143 1429809190
6592509372 2169646151 5709858387 4105978859 5977297549
8930161753 9284681382 6868386894 2774155991 8559252459
5395943104 9972524680 8459872736 4469584865 3836736222
6260991246 0805124388 4390451244 1365497627 8079771569
1435997700 1296160894 4169486855 5848406353 4220722258
2848864815 8456028506 0168427394 5226746767 8895252138
5225499546 6672782398 6456596116 3548862305 7745649803
5593634568 1743241125 1507606947 9451096596 0940252288
7971089314 5669136867 2287489405 6010150330 8617928680
9208747609 1782493858 9009714909 6759852613 6554978189
3129784821 6829989487 2265880485 7564014270 4775551323
7964145152 3746234364 5428584447 9526586782 1051141354
7357395231 1342716610 2135969536 2314429524 8493718711
0145765403 5902799344 0374200731 0578539062 1983874478
0847848968 3321445713 8687519435 0643021845 3191048481
0053706146 8067491927 8191197939 9520614196 6342875444
0643745123 7181921799 9839101591 9561814675 1426912397
4894090718 6494231961 5679452080 9514655022 5231603881
9301420937 6213785595 6638937787 0830390697 9207734672
2182562599 6615014215 0306803844 7734549202 6054146659
2520149744 2850732518 6660021324 3408819071 0486331734
6496514539 0579626856 1005508106 6587969981 6357473638
4052571459 1028970641 4011097120 6280439039 7595156771
5770042033 7869936007 2305587631 7635942187 3125147120
5329281918 2618612586 7321579198 4148488291 6447060957
5270695722 0917567116 7229109816 9091528017 3506712748
5832228718 3520935396 5725121083 5791513698 8209144421
0067510334 6711031412 6711136990 8658516398 3150197016
5151168517 1437657618 3515565088 4909989859 9823873455
2833163550 7647918535 8932261854 8963213293 3089857064
2046752590 7091548141 6549859461 6371802709 8199430992
4488957571 2828905923 2332609729 9712084433 5732654893
8239119325 9746366730 5836041428 1388303203 8249037589
8524374417 0291327656 1809377344 4030707469 2112019130
2033038019 7621101100 4492932151 6084244485 9637669838
9522868478 3123552658 2131449576 8572624334 4189303968
6426243410 7732269780 2807318915 4411010446 8232527162
0105265227 2111660396 6655730925 4711055785 3763466820
6531098965 2691862056 4769312570 5863566201 8558100729
3606598764 8611791045 3348850346 1136576867 5324944166
8039626579 7877185560 8455296541 2665408530 6143444318
5867697514 5661406800 7002378776 5913440171 2749470420
5622305389 9456131407 1127000407 8547332699 3908145466
4645880797 2708266830 6343285878 5698305235 8089330657
5740679545 7163775254 2021149557 6158140025 0126228594
1302164715 5097925923 0990796547 3761255176 5675135751
7829666454 7791745011 2996148903 0463994713 2962107340
4375189573 5961458901 9389713111 7904297828 5647503203
1986915140 2870808599 0480109412 1472213179 4764777262
2414254854 5403321571 8530614228 8137585043 0633217518
2979866223 7172159160 7716692547 4873898665 4949450114
6540628433 6639379003 9769265672 1463853067 3609657120
9180763832 7166416274 8888007869 2560290228 4721040317
2118608204 1900042296 6171196377 9213375751 1495950156
6049631862 9472654736 4252308177 0367515906 7350235072
8354056704 0386743513 6222247715 8915049530 9844489333
0963408780 7693259939 7805419341 4473774418 4263129860
8099888687 4132604721 5695162396 5864573021 6315981931
9516735381 2974167729 4786724229 2465436680 0980676928
2382806899 6400482435 4037014163 1496589794 0924323789
6907069779 4223625082 2168895738 3798623001 5937764716
5122893578 6015881617 5578297352 3344604281 5126272037
3431465319 7777416031 9906655418 7639792933 4419521541
3418994854 4473456738 3162499341 9131814809 2777710386
3877343177 2075456545 3220777092 1201905166 0962804909
2636019759 8828161332 3166636528 6193266863 3606273567
6303544776 2803504507 7723554710 5859548702 7908143562
4014517180 6246436267 9456127531 8134078330 3362542327
8394497538 2437205835 3114771199 2606381334 6776879695
9703098339 1307710987 0408591337 4641442822 7726346594
7047458784 7787201927 7152807317 6790770715 7213444730
6057007334 9243693113 8350493163 1284042512 1925651798
0694113528 0131470130 4781643788 5185290928 5452011658
3934196562 1349143415 9562586586 5570552690 4965209858
0338507224 2648293972 8584783163 0577775606 8887644624
8246857926 0395352773 4803048029 0058760758 2510474709
1643961362 6760449256 2742042083 2085661190 6254543372
1315359584 5068772460 2901618766 7952406163 4252257719
5429162991 9306455377 9914037340 4328752628 8896399587
9475729174 6426357455 2540790914 5135711136 9410911939
3251910760 2082520261 8798531887 7058429725 9167781314
9699009019 2116971737 2784768472 6860849003 3770242429
1651300500 5168323364 3503895170 2989392233 4517220138
1280696501 1784408745 1960121228 5993716231 3017114448
4640903890 6449544400 6198690754 8516026327 5052983491
8740786680 8818338510 2283345085 0486082503 9302133219
7155184306 3545500766 8282949304 1377655279 3975175461
3953984683 3936383047 4611996653 8581538420 5685338621
8672523340 2830871123 2827892125 0771262946 3229563989
8989358211 6745627010 2183564622 0134967151 8819097303
8119800497 3407239610 3685406643 1939509790 1906996395
5245300545 0580685501 9567302292 1913933918 5680344903
9820595510 0226353536 1920419947 4553859381 0234395544
9597783779 0237421617 2711172364 3435439478 2218185286
2408514006 6604433258 8856986705 4315470696 5747458550
3323233421 0730154594 0516553790 6866273337 9958511562
5784322988 2737231989 8757141595 7811196358 3300594087
3068121602 8764962867 4460477464 9159950549 7374256269
0104903778 1986835938 1465741268 0492564879 8556145372
3478673303 9046883834 3634655379 4986419270 5638729317
4872332083 7601123029 9113679386 2708943879 9362016295
1541337142 4892830722 0126901475 4668476535 7616477379
4675200490 7571555278 1965362132 3926406160 1363581559
0742202020 3187277605 2772190055 6148425551 8792530343
5139844253 2234157623 3610642506 3904975008 6562710953
5919465897 5141310348 2276930624 7435363256 9160781547
8181152843 6679570611 0861533150 4452127473 9245449454
2368288606 1340841486 3776700961 2071512491 4043027253
8607648236 3414334623 5189757664 5216413767 9690314950
1910857598 4423919862 9164219399 4907236234 6468441173
9403265918 4044378051 3338945257 4239950829 6591228508
5558215725 0310712570 1266830240 2929525220 1187267675
6220415420 5161841634 8475651699 9811614101 0029960783
8690929160 3028840026 9104140792 8862150784 2451670908
7000699282 1206604183 7180653556 7252532567 5328612910
4248776182 5829765157 9598470356 2226293486 0034158722
9805349896 5022629174 8788202734 2092222453 3985626476
6914905562 8425039127 5771028402 7998066365 8254889264
8802545661 0172967026 6407655904 2909945681 5065265305
3718294127 0336931378 5178609040 7086671149 6558343434
7693385781 7113864558 7367812301 4587687126 6034891390
9562009939 3610310291 6161528813 8437909904 2317473363
9480457593 1493140529 7634757481 1935670911 0137751721
0080315590 2485309066 9203767192 2033229094 3346768514
2214477379 3937517034 4366199104 0337511173 5471918550
4644902636 5512816228 8244625759 1633303910 7225383742
1821408835 0865739177 1509682887 4782656995 9957449066
1758344137 5223970968 3408005355 9849175417 3818839994
4697486762 6551658276 5848358845 3142775687 9002909517
0283529716 3445621296 4043523117 6006651012 4120065975
5851276178 5838292041 9748442360 8007193045 7618932349
2292796501 9875187212 7267507981 2554709589 0455635792
1221033346 6974992356 3025494780 2490114195 2123828153
0911407907 3860251522 7429958180 7247162591 6685451333
1239480494 7079119153 2673430282 4418604142 6363954800
0448002670 4962482017 9289647669 7583183271 3142517029
6923488962 7668440323 2609275249 6035799646 9256504936
8183609003 2380929345 9588970695 3653494060 3402166544
3755890045 6328822505 4525564056 4482465151 8754711962
1844396582 5337543885 6909411303 1509526179 3780029741
2076651479 3942590298 9695946995 5657612186 5619673378
6236256125 2163208628 6922210327 4889218654 3648022967
8070576561 5144632046 9279068212 0738837781 4233562823
6089632080 6822246801 2248261177 1858963814 0918390367
3672220888 3215137556 0037279839 4004152970 0287830766
7094447456 0134556417 2543709069 7939612257 1429894671
5435784687 8861444581 2314593571 9849225284 7160504922
1242470141 2147805734 5510500801 9086996033 0276347870
8108175450 1193071412 2339086639 3833952942 5786905076
4310063835 1983438934 1596131854 3475464955 6978103829
3097164651 4384070070 7360411237 3599843452 2516105070
2705623526 6012764848 3084076118 3013052793 2054274628
6540360367 4532865105 7065874882 2569815793 6789766974
2205750596 8344086973 5020141020 6723585020 0724522563
2651341055 9240190274 2162484391 4035998953 5394590944
0704691209 1409387001 2645600162 3742880210 9276457931
0657922955 2498872758 4610126483 6999892256 9596881592
0560010165 5256375678 | Version 1.4.1
| |
For Automotive Calculators, Converters and
Tables For Aviation Calculators, Converters and
Tables For Communications Calculators, Converters and
Tables For Computer Calculators, Converters and
Tables For Construction And Remodel Calculators, Converters and
Tables For Electronics Calculators, Converters and
Tables For Business And Financial Calculators, Converters and
Tables For General Interest Calculators, Converters and
Tables For
Health Calculators, Converters and Tables For
Lottery Calculators, Converters and Tables For
Pure Educational Math Converters and Calculators For Science Calculators, Converters and
Tables For Small Game Simulator Calculators, Converters and
Tables For
Sports Calculators, Converters and Tables For
Subroutines And Snippets Source Code For Converters and
Calculators For
Time Calculators, Converters and Tables
Of Special Interest
|