Π or π (or in English, "pi") is the 16th letter of the Greek alphabet.

The upper case form, Π , means:

The lower case form, π , means:

As the top of this e2node indicates, pi is also an Everythingite.

What is pi?

Pi is the number equal to the circumference divided by the diameter of a circle. It's an irrational number so most people just use 3.14 or 3.14159. Though many memorize a lot more (hundreds) of digits, nobody is stupid enough to try to multiply by that.

The circumference of a circle is πR2 (R=Radius) or just πD (D=diameter).
The area of a circle is πR2.

See A brief history of Pi for, well, the history of pi.

Also the title of a poem which I first saw as an easter egg on Audiofind.com. Sadly I have no idea who the original poet was.

i knelt down next to you
watched you laying there
it's time to wake up
there are a lot of people who want to meet you

you looked back at me
stared into my eyes
i'll never forget what you said
"you"
"you are the builder"
"the creator of things unseen"

An attempt at a complete list. This is one overworked letter. :)

1. The 16th letter of the Greek alphabet.
2. Ancient Greek term for the circumference of a circle.
3. Modern term, as N-wing mentioned, for the irrational ratio of a circle's diameter to its circumference. This ratio pops up in many other places too.
4. N-wing states population percentage in statistics. I'll take his word for it.
5. Product series when capitalized. As in, Π(1<x<5) of (x-1), x in Z =(2-1)(3-1)(4-1)
6. π(x) is the number of primes below a number x - for example, π(100) = 25 (this, btw, approaches x/ln(x))

Given its general popularity as a concept meaning product, I'm sure there are other uses in various sciences. Will keep on hunting. Just had to add #6, my personal area of obsession.

15,000? HA! here's the first 58,688 decimal places of pi:

3.141592653589793238462643383279 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 5667227966 1988578279 4848855834 3975187445 4551296563 4434803966
4205579829 3680435220 2770984294 2325330225 7634180703 9476994159 7915945300 6975214829
3366555661 5678736400 5366656416 5473217043 9035213295 4352916941 4599041608 7532018683
7937023488 8689479151 0716378529 0234529244 0773659495 6305100742 1087142613 4974595615
1384987137 5704710178 7957310422 9690666702 1449863746 4595280824 3694457897 7233004876
4765241339 0759204340 1963403911 4732023380 7150952220 1068256342 7471646024 3354400515
2126693249 3419673977 0415956837 5355516673 0273900749 7297363549 6453328886 9844061196
4961627734 4951827369 5588220757 3551766515 8985519098 6665393549 4810688732 0685990754
0792342402 3009259007 0173196036 2254756478 9406475483 4664776041 1463233905 6513433068
4495397907 0903023460 4614709616 9688688501 4083470405 4607429586 9913829668 2468185710
3188790652 8703665083 2431974404 7718556789 3482308943 1068287027 2280973624 8093996270
6074726455 3992539944 2808113736 9433887294 0630792615 9599546262 4629707062 5948455690
3471197299 6409089418 0595343932 5123623550 8134949004 3642785271 3831591256 8989295196
4272875739 4691427253 4366941532 3610045373 0488198551 7065941217 3524625895 4873016760
0298865925 7866285612 4966552353 3829428785 4253404830 8330701653 7228563559 1525347844
5981831341 1290019992 0598135220 5117336585 6407826484 9427644113 7639386692 4803118364
4536985891 7544264739 9882284621 8449008777 6977631279 5722672655 5625962825 4276531830
0134070922 3343657791 6012809317 9401718598 5999338492 3549564005 7099558561 1349802524
9906698423 3017350358 0440811685 5265311709 9570899427 3287092584 8789443646 0050410892
2669178352 5870785951 2983441729 5351953788 5534573742 6085902908 1765155780 3905946408
7350612322 6112009373 1080485485 2635722825 7682034160 5048466277 5045003126 2008007998
0492548534 6941469775 1649327095 0493463938 2432227188 5159740547 0214828971 1177792376
1225788734 7718819682 5462981268 6858170507 4027255026 3329044976 2778944236 2167411918
6269439650 6715157795 8675648239 9391760426 0176338704 5499017614 3641204692 1823707648
8783419689 6861181558 1587360629 3860381017 1215855272 6683008238 3404656475 8804051380
8016336388 7421637140 6435495561 8689641122 8214075330 2655100424 1048967835 2858829024
3670904887 1181909094 9453314421 8287661810 3100735477 0549815968 0772009474 6961343609
2861484941 7850171807 7930681085 4690009445 8995279424 3981392135 0558642219 6483491512
6390128038 3200109773 8680662877 9239718014 6134324457 2640097374 2570073592 1003154150
8936793008 1699805365 2027600727 7496745840 0283624053 4603726341 6554259027 6018348403
0681138185 5105979705 6640075094 2608788573 5796037324 5141467867 0368809880 6097164258
4975951380 6930944940 1515422221 9432913021 7391253835 5915031003 3303251117 4915696917
4502714943 3151558854 0392216409 7229101129 0355218157 6282328318 2342548326 1119128009
2825256190 2052630163 9114772473 3148573910 7775874425 3876117465 7867116941 4776421441
1112635835 5387136101 1023267987 7564102468 2403226483 4641766369 8066378576 8134920453
0224081972 7856471983 9630878154 3221166912 2464159117 7673225326 4335686146 1865452226
8126887268 4459684424 1610785401 6768142080 8850280054 1436131462 3082102594 1737562389
9420757136 2751674573 1891894562 8352570441 3354375857 5342698699 4725470316 5661399199
9682628247 2706413362 2217892390 3176085428 9437339356 1889165125 0424404008 9527198378
7386480584 7268954624 3882343751 7885201439 5600571048 1194988423 9060613695 7342315590
7967034614 9143447886 3604103182 3507365027 7859089757 8272731305 0488939890 0992391350
3373250855 9826558670 8924261242 9473670193 9077271307 0686917092 6462548423 2407485503
6608013604 6689511840 0936686095 4632500214 5852930950 0009071510 5823626729 3264537382
1049387249 9669933942 4685516483 2611341461 1068026744 6637334375 3407642940 2668297386
5220935701 6263846485 2851490362 9320199199 6882851718 3953669134 5222444708 0459239660
2817156551 5656661113 5982311225 0628905854 9145097157 5539002439 3153519090 2107119457
3002438801 7661503527 0862602537 8817975194 7806101371 5004489917 2100222013 3501310601
6391541589 5780371177 9277522597 8742891917 9155224171 8958536168 0594741234 1933984202
1874564925 6443462392 5319531351 0331147639 4911995072 8584306583 6193536932 9699289837
9149419394 0608572486 3968836903 2655643642 1664425760 7914710869 9843157337 4964883529
2769328220 7629472823 8153740996 1545598798 2598910937 1712621828 3025848112 3890119682
2142945766 7580718653 8065064870 2613389282 2994972574 5303328389 6381843944 7707794022
8435988341 0035838542 3897354243 9564755568 4095224844 5541392394 1000162076 9363684677
6413017819 6593799715 5746854194 6334893748 4391297423 9143365936 0410035234 3777065888
6778113949 8616478747 1407932638 5873862473 2889645643 5987746676 3847946650 4074111825
6583788784 5485814896 2961273998 4134427260 8606187245 5452360643 1537101127 4680977870
4464094758 2803487697 5894832824 1239292960 5829486191 9667091895 8089833201 2103184303
4012849511 6203534280 1441276172 8583024355 9830032042 0245120728 7253558119 5840149180
9692533950 7577840006 7465526031 4461670508 2768277222 3534191102 6341631571 4740612385
0425845988 4199076112 8725805911 3935689601 4316682831 7632356732 5417073420 8173322304
6298799280 4908514094 7903688786 8789493054 6955703072 6190095020 7643349335 9106024545
0864536289 3545686295 8531315337 1838682656 1786227363 7169757741 8302398600 6591481616
4049449650 1173213138 9574706208 8474802365 3710311508 9842799275 4426853277 9743113951
4357417221 9759799359 6852522857 4526379628 9612691572 3579866205 7340837576 6873884266
4059909935 0500081337 5432454635 9675048442 3528487470 1443545419 5762584735 6421619813
4073468541 1176688311 8654489377 6979566517 2796623267 1481033864 3913751865 9467300244
3450054499 5399742372 3287124948 3470604406 3471606325 8306498297 9551010954 1836235030
3094530973 3583446283 9476304775 6450150085 0757894954 8931393944 8992161255 2559770143
6858943585 8775263796 2559708167 7643800125 4365023714 1278346792 6101995585 2247172201
7772370041 7808419423 9487254068 0155603599 8390548985 7235467456 4239058585 0216719031
3952629445 5439131663 1345308939 0620467843 8778505423 9390524731 3620129476 9187497519
1011472315 2893267725 3391814660 7300089027 7689631148 1090220972 4520759167 2970078505
8071718638 1054967973 1001678708 5069420709 2232908070 3832634534 5203802786 0990556900
1341371823 6837099194 9516489600 7550493412 6787643674 6384902063 9640197666 8559233565
4639138363 1857456981 4719621084 1080961884 6054560390 3845534372 9141446513 4749407848
8442377217 5154334260 3066988317 6833100113 3108690421 9390310801 4378433415 1370924353
0136776310 8491351615 6422698475 0743032971 6746964066 6531527035 3254671126 6752246055
1199581831 9637637076 1799191920 3579582007 5956053023 4626775794 3936307463 0569010801
1494271410 0939136913 8107258137 8135789400 5599500183 5425118417 2136055727 5221035268
0373572652 7922417373 6057511278 8721819084 4900617801 3889710770 8229310027 9766593583
8758909395 6881485602 6322439372 6562472776 0378908144 5883785501 9702843779 3624078250
5270487581 6470324581 2908783952 3245323789 6029841669 2254896497 1560698119 2186584926
7704039564 8127810217 9913217416 3058105545 9880130048 4562997651 1212415363 7451500563
5070127815 9267142413 4210330156 6165356024 7338078430 2865525722 2753049998 8370153487
9300806260 1809623815 1613669033 4111138653 8510919367 3938352293 4588832255 0887064507
5394739520 4396807906 7086806445 0969865488 0168287434 3786126453 8158342807 5306184548
5903798217 9945996811 5441974253 6344399602 9025100158 8827216474 5006820704 1937615845
4712318346 0072629339 5505482395 5713725684 0232268213 0124767945 2264482091 0235647752
7230820810 6351889915 2692889108 4555711266 0396503439 7896278250 0161101532 3516051965
5904211844 9499077899 9200732947 6905868577 8787209829 0135295661 3978884860 5097860859
5701773129 8155314951 6814671769 5976099421 0036183559 1387778176 9845875810 4466283998
8060061622 9848616935 3373865787 7359833616 1338413385 3684211978 9389001852 9569196780
4554482858 4837011709 6721253533 8758621582 3101331038 7766827211 5726949518 1795897546
9399264219 7915523385 7662316762 7547570354 6994148929 0413018638 6119439196 2838870543
6777432242 7680913236 5449485366 7680000010 6526248547 3055861598 9991401707 6983854831
8875014293 8908995068 5453076511 6803337322 2651756622 0752695179 1442252808 1651716677
6672793035 4851542040 2381746089 2328391703 2754257508 6765511785 9395002793 3895920576
6827896776 4453184040 4185540104 3513483895 3120132637 8369283580 8271937831 2654961745
9970567450 7183320650 3455664403 4490453627 5600112501 8433560736 1222765949 2783937064
7842645676 3388188075 6561216896 0504161139 0390639601 6202215368 4941092605 3876887148
3798955999 9112099164 6464411918 5682770045 7424343402 1672276445 5893301277 8158686952
5069499364 6101756850 6016714535 4315814801 0545886056 4550133203 7586454858 4032402987
1709348091 0556211671 5468484778 0394475697 9804263180 9917564228 0987399876 6973237695
7370158080 6822904599 2123661689 0259627304 3067931653 1149401764 7376938735 1409336183
3216142802 1497633991 8983548487 5625298752 4238730775 5955595546 5196394401 8218409984
1248982623 6737714672 2606163364 3296406335 7281070788 7581640438 1485018841 1431885988
2769449011 9321296827 1588841338 6943468285 9006664080 6314077757 7257056307 2940049294
0302420498 4165654797 3670548558 0445865720 2276378404 6682337985 2827105784 3197535417
9501134727 3625774080 2134768260 4502285157 9795797647 4670228409 9956160156 9108903845
8245026792 6594205550 3958792298 1852648007 0683765041 8365620945 5543461351 3415257006
5974881916 3413595567 1964965403 2187271602 6485930490 3978748958 9066127250 7948282769
3895352175 3621850796 2977851461 8843271922 3223810158 7444505286 6523802253 2843891375
2738458923 8442253547 2653098171 5784478342 1582232702 0690287232 3300538621 6347988509
4695472004 7952311201 5043293226 6282727632 1779088400 8786148022 1475376578 1058197022
2630971749 5072127248 4794781695 7296142365 8595782090 8307332335 6034846531 8730293026
6596450137 1837542889 7557971449 9246540386 8179921389 3469244741 9850973346 2679332107
2686870768 0626399193 6196504409 9542167627 8409146698 5692571507 4315740793 8053239252
3947755744 1591845821 5625181921 5523370960 7483329234 9210345146 2643744980 5596103307
9941453477 8457469999 2128599999 3996122816 1521931488 8769388022 2810830019 8601654941
6542616968 5867883726 0958774567 6182507275 9929508931 8052187292 4610867639 9589161458
5505839727 4209809097 8172932393 0106766386 8240401113 0402470073 5085782872 4627134946
3685318154 6969046696 8693925472 5194139929 1465242385 7762550047 4852954768 1479546700
7050347999 5888676950 1612497228 2040303995 4632788306 9597624936 1510102436 5553522306
9061294938 8599015734 6610237122 3547891129 2547696176 0050479749 2806072126 8039226911
0277722610 2544149221 5765045081 2067717357 1202718024 2968106203 7765788371 6690910941
8074487814 0490755178 2038565390 9910477594 1413215432 8440625030 1802757169 6508209642
7348414695 7263978842 5600845312 1406593580 9041271135 9200419759 8513625479 6160632288
7361813673 7324450607 9244117639 9759746193 8358457491 5988097667 4470930065 4634242346
0634237474 6660804317 0126005205 5928493695 9414340814 6852981505 3947178900 4518357551
5412522359 0590687264 8786357525 4191128887 7371766374 8602766063 4960353679 4702692322
9718683277 1739323619 2007774522 1262475186 9833495151 0198642698 8784717193 9664976907
0825217423 3656627259 2844062043 0214113719 9227852699 8469884770 2323823840 0556555178
8908766136 0130477098 4386116870 5231055314 9162517283 7327286760 0724817298 7637569816
3354150746 0883866364 0693470437 2066886512 7568826614 9730788657 0156850169 1864748854
1679154596 5072342877 3069985371 3904300266 5307839877 6385032381 8215535597 3235306860
4301067576 0838908627 0498418885 9513809103 0423595782 4951439885 9011318583 5840667472
3702971497 8508414585 3085781339 1562707603 5639076394 7311455495 8322669457 0249413983
1634332378 9759556808 5683629725 3867913275 0555425244 9194358912 8405045226 9538121791
3191451350 0993846311 7740179715 1228378546 0116035955 4028644059 0249646693 0707769055
4810288502 0808580087 8115773817 1917417760 1733073855 4758006056 0143377432 9901272867
7253043182 5197579167 9296996504 1460706645 7125888346 9797964293 1622965520 1687973000
3564630457 9308840327 4807718115 5533090988 7025505207 6804630346 0865816539 4876951960
0440848206 5967379473 1680864156 4565053004 9881616490 5788311543 4548505266 0069823093
1577765003 7807046612 6470602145 7505793270 9620478256 1524714591 8965223608 3966456241
0519551052 2357239739 5128818164 0597859142 7914816542 6328920042 8160913693 7773722299
9833270820 8296995573 7727375667 6155271139 2258805520 1898876201 1416800546 8736558063
3471603734 2917039079 8639652296 1312801782 6797172898 2293607028 8069087768 6605932527
4637840539 7691848082 0410219447 1971386925 6084162451 1239806201 1318454124 4782050110
7987607171 5568315407 8865439041 2108730324 0201068534 1947230476 6667217498 6986854707
6781205124 7367924791 9315085644 4775379853 7997322344 5612278584 3296846647 5133365736
9238720146 4723679427 8700425032 5558992688 4349592876 1240075587 5694641370 5625140011
7971331662 0715371543 6006876477 3186755871 4878398908 1074295309 4106059694 4315847753
9700943988 3949144323 5366853920 9946879645 0665339857 3888786614 7629443414 0104988899
3160051207 6781035886 1166020296 1193639682 1349607501 1164983278 5635316145 1684576956
8710900299 9769841263 2665023477 1672865737 8579085746 6460772283 4154031144 1529418804
7825438761 7707904300 0156698677 6795760909 9669360755 9496515273 6349811896 4130433116
6277471233 8817406037 3174397054 0670310967 6765748695 3587896700 3192586625 9410510533
5843846560 2339179674 9267844763 7084749783 3365557900 7384191473 1988627135 2595462518
1604342253 7299628632 6749682405 8060296421 1463864368 6422472488 7283434170 4415734824
8183330164 0566959668 8667695634 9141632842 6414974533 3499994800 0266998758 8815935073
5781519588 9900539512 0853510357 2613736403 4367534714 1048360175 4648830040 7846416745
2167371904 8310967671 1344349481 9262681110 7399482506 0739495073 5031690197 3185211955
2635632584 3390998224 9862406703 1076831844 6607291248 7475403161 7969941139 7387765899
8685541703 1884778867 5929026070 0432126661 7919223520 9382278788 8098863359 9116081923
5355570464 6349113208 5918979613 2791319756 4909760001 3996234445 5350143464 2686046449
5862476909 4347048293 2941404111 4654092398 8344435159 1332010773 9441118407 4107684981
0663472410 4823935827 4019449356 6516108846 3125678529 7769734684 3030614624 1803585293
3159734583 0384554103 3701091676 7763742762 1021370135 4854450926 3071901147 3184857492
3318167207 2137279355 6795284439 2548156091 3728128406 3330393735 6242001604 5664557414
5881660521 6660873874 8047243391 2129558777 6390696903 7078828527 7538940524 6075849623
1574369171 1317613478 3882719416 8606625721 0368513215 6647800147 6752310393 5786068961
1125996028 1839309548 7090590738 6135191459 1819510297 3278755710 4972901148 7171897180
0469616977 7001791391 9613791417 1627070189 5846921434 3696762927 4591099400 6008498356
8425201915 5937037010 1104974733 9493877885 9894174330 3178534870 7603221982 9705797511
9144051099 4235883034 5463534923 4982688362 4043327267 4155403016 1950568065 4180939409
9820206099 9414021689 0900708213 3072308966 2119775530 6659188141 1915778362 7292746156
1857103721 7247100952 1423696483 0864102592 8874579993 2237495519 1221951903 4244523075
3513380685 6807354464 9951272031 7448719540 3976107308 0602699062 5807602029 2731455252
0780799141 8429063884 4373499681 4582733720 7266391767 0201183004 6481900024 1308350884
6584152148 9912761065 1374153943 5657211390 3285749187 6909441370 2090517031 4877734616
5287984823 5338297260 1361109845 1484182380 8120540996 1252745808 8109948697 2216128524
8974255555 1607637167 5054896173 0168096138 0381191436 1143992106 3800508321 4098760459
9309324851 0251682944 6726066613 8151745712 5597549535 8023998314 6982203613 3808284993
5670557552 4712902745 3977621404 9318201465 8008021566 5360677655 0878380430 4134310591
8046068008 3459113664 0834887408 0057412725 8670479225 8319127415 7390809143 8313845642
4150940849 1339180968 4025116399 1936853225 5573389669 5374902662 0923261318 8558915808
3245557194 8453875628 7861288590 0410600607 3746501402 6278240273 4696252821 7174941582
3317492396 8353013617 8653673760 6421667781 3773995100 6589528877 4276626368 4183068019
0804609849 8094697636 6733566228 2915132352 7888061577 6827815958 8669180238 9403330764
4191240341 2022316368 5778603572 7694154177 8826435238 1319050280 8701857504 7046312933
3537572853 8660588890 4583111450 7739429352 0199432197 1171642235 0056440429 7989208159
4307167019 8574692738 4865383343 6145794634 1759225738 9858800169 8014757420 5429958012
4295810545 6510831046 2972829375 8416116253 2562516572 4980784920 9989799062 0035936509
9347215829 6517413579 8491047111 6607915874 3698654122 2348341887 7229294463 3517865385
6731962559 8520260729 4767407261 6767145573 6498121056 7771689348 4917660771 7052771876
0119990814 4113058645 5779105256 8430481144 0261938402 3224709392 4980293355 0731845890
3553971330 8844617410 7959162511 7148648744 6861124760 5428673436 7090466784 6867027409
1881014249 7111496578 1772427934 7070216688 2956108777 9440504843 7528443375 1088282647
7197854000 6509704033 0218625561 4733211777 1174413350 2816088403 5178145254 1964320309
5760186946 4908868154 5285621346 9883554445 6024955666 8436602922 1951248309 1060537720
1980218310 1032704178 3866544718 1260397190 6884623708 5751808003 5327047185 6594994761
2424811099 9288679158 9690495639 4762460842 4065930948 6215076903 1498702067 3533848349
5508363660 1784877106 0809804269 2471324100 0946401437 3603265645 1845667924 5666955100
1502298330 7984960799 4988249706 1723674493 6122622296 1790814311 4146609412 3415935930
9585407913 9087208322 7335495720 8075716517 1876599449 8569379562 3875551617 5754380917
8052802946 4200447215 3962807463 6021132942 5591600257 0735628126 3873310600 5891065245
7080244749 3754318414 9401482119 9962764531 0680066311 8382376163 9663180931 4446712986
1552759820 1451410275 6006892975 0246304017 3514891945 7636078935 2855505317 3314164570
5049964438 9093630843 8744847839 6168405184 5273288403 2345202470 5685164657 1647713932
3775517294 7951261323 9822960239 4548579754 5865174587 8771331813 8752959809 4121742273
0035229650 8089177705 0682592488 2232215493 8048371454 7816472139 7682096332 0508305647
9204820859 2047549985 7320388876 3916019952 4091893894 5576768749 7308569559 5801065952
6503036266 1597506622 2508406742 8898265907 5106375635 6996821151 0949669744 5805472886
9363102036 7823250182 3237084597 9011154847 2087618212 4778132663 3041207621 6587312970
8112307581 5982124863 9807212407 8688781145 0165582513 6178903070 8608701989 7588980745
6643955157 4153631931 9198107057 5336633738 0382721527 9884935039 7480015890 5194208797
1130805123 3933221903 4662499171 6915094854 1401871060 3546037946 4337900589 0957721180
8044657439 6280618671 7861017156 7409676620 8029576657 7051291209 9079443046 3289294730
6159510430 9022214393 7184956063 4056189342 5130572682 9146578329 3340524635 0289291754
7087256484 2600349629 6116541382 3007731332 7298305001 6025672401 4185152041 8907011542
8857992081 2198449315 6999059182 0118197335 0012618772 8036812481 9958770702 0753240636
1259313438 5955425477 8196114293 5163561223 4966615226 1473539967 4051584998 6035529533
2924575238 8810136202 3476246690 5581643896 7863097627 3655047243 4864307121 8494373485
3006063876 4456627218 6661701238 1277156213 7974614986 1328744117 7145524447 0899714452
2885662942 4402301847 9120547849 8574521634 6964489738 9206240194 3518310088 2834802492
4908540307 7863875165 9113028739 5878709810 0772718271 8745290139 7283661484 2142871705
5317965430 7650453432 4600536361 4726181809 6997693348 6264077435 1999286863 2383508875
6683595097 2655748154 3194019557 6850437248 0010204137 4983187225 9677387154 9583997184
4490727914 1965845930 0839426370 2087563539 8216962055 3248032122 6749891140 2678528599
6734052420 3109179789 9905718821 9493913207 5343170798 0023736590 9853755202 3891164346
7185582906 8537118979 5262623449 2483392496 3424497146 5684659124 8918556629 5893299090
3523923333 3647435203 7077010108 4388003290 7598342170 1855422838 6161721041 7603011645
9187805393 6744747205 9985023582 8918336929 2233732399 9480437108 4196594731 6265482574
8099482509 9918330069 7656936715 9689364493 3488647442 1350084070 0660883597 2350395323
4017958255 7036016936 9909886711 3210979889 7070517280 7558551912 6993067309 9250704070
2455685077 8679069476 6126298082 2516331363 9952117098 4528092630 3759224267 4257559989
2892783704 7444521893 6320348941 5521044597 2618838003 0067761793 1381399162 0580627016
5102445886 9247649246 8919246121 2531027573 1390840470 0071435613 6231699237 1694848132
5542009145 3041037135 4532966206 3921054798 2439212517 2540132314 9027405858 9206321758
9494345489 0684639931 3757091034 6332714153 1622328055 2297297953 8018801628 5907357295
5416278867 6498274186 1642187898 8574107164 9069191851 1628152854 8679417363 8906653885
7642291583 4250067361 2453849160 6741373401 7357277995 6341043326 8835695078 1493137800
7362354180 0706191802 6732855119 1942676091 2210359874 6924117283 7493126163 3950012395
9924050845 4375698507 9570462226 6461900010 3500490183 0341535458 4283376437 8111988556
3187777925 3720116671 8539541835 9844383052 0376281944 0761594106 8207169703 0228515225
0573126093 0468984234 3315273213 1361216582 8080752126 3154773060 4423774753 5059522871
7440266638 9148817173 0864361113 8906942027 9088143119 4487994171 5404210341 2190847094
0802540239 3294294549 3878640230 5129271190 9751353600 0921971105 4120966831 1151632870
5423028470 0731206580 3262641711 6165957613 2723515666 6253667271 8998534199 8952368848
3099930275 7419916463 8414270779 8870887422 9277053891 2271724863 2202889842 5125287217
8260305009 9451082478 3572905691 9885554678 8607946280 5371227042 4665431921 4528176074
1482403827 8358297193 0101788834 5674167811 3989547504 4833931468 9630763396 6572267270
4339321674 5421824557 0625247972 1997866854 2798977992 3395790575 8189062252 5473582205
2364248507 8340711014 4980478726 6919901864 3882293230 5382318559 7328697809 2225352959
1017341407 3348847610 0556401824 2392192695 0620831838 1454698392 3664613639 8910121021
7709597670 4908305081 8547041946 6437131229 9692358895 3849301363 5657618610 6062228705
5994233716 3102127845 7446463989 7381885667 4626087948 2018647487 6727272220 6267646533
8099801966 8836809941 5907577685 2639865146 2533363124 5053640261 0569605513 1838131742
6118442018 9088853196 3569869627 9503673842 4313011331 7533053298 0201668881 7481342988
6815855778 1034323175 3064784983 2106297184 2518438553 4427620128 2345707169 8853051832
6179641178 5796088881 5032960229 0705614476 2209150947 3903594664 6916235396 8092013945
7817589108 8931992112 2600739281 4916948161 5273842736 2642980982 3406320024 4024495894
4561291670 4950823581 2487391799 6486411334 8032475777 5219708932 7722623494 8601504665
2681439877 0516153170 2669692970 4928316285 5042128981 4670619533 1970269507 2143782304
7687528028 7354126166 3917082459 2517001071 4180854800 6369232594 6201900227 8087409859
7719218051 5853214739 2653251559 0354102092 8466592529 9914353791 8253145452 9059841581
7637058927 9069098969 1116438118 7809435371 5213322614 4362531449 0127454772 6957393934
8154691631 1624928873 5747188240 7150399500 9446731954 3161938554 8520766573 8825139639
1635767231 5100555603 7263394867 2082078086 5373494244 0115799667 5073607111 5935133195
9197120948 9647175530 2453136477 0942094635 6969822266 7377520994 5168450643 6238242118
5353488798 9395673187 8066061078 8544000550 8276570305 5874485418 0577889171 9207881423
3511386629 2966717964 3468760077 0479995378 8338787034 8718021842 4373421122 7394025571
7690819603 0920182401 8842705704 6092622564 1783752652 6335832424 0661253311 5294234579
6556950250 6810018310 9004112453 7901533296 6156970522 3792103257 0693705109 0830789479
9990049993 9532215362 2748476603 6136776979 7856738658 4670936679 5885837887 9562594646
4891376652 1995882869 3380183601 1932368578 5585581955 5604215625 0883650203 3220245137
6215820461 8106705195 3306530606 0650105488 7167245377 9428313388 7163139559 6905832083
4168984760 6560711834 7136218123 2462272588 4199028614 2087284956 8796393254 6428534307
5301105285 7138296437 0999035694 8885285190 4029560473 4613113826 3878897551 7885604249
9874831638 2804046848 6189381895 9054203988 9872650697 6202019955 4841265000 5394428203
9301274816 3815853039 6439925470 2016727593 2857436666 1644110962 5663373054 0921951967
5148328734 8089574777 7527834422 1091073111 3518280460 3634719818 5655572957 1447476825
5285786334 9342858423 1187494400 0322969069 7758315903 8580393535 2135886007 9600342097
5473922967 3331064939 5601812237 8128545843 1760556173 3861126734 7807458506 7606304822
9409653041 1183066710 8189303110 8871728167 5195796753 4718853722 9309616143 2040063813
2246584111 1157758358 5811350185 6904781536 8938137718 4728147519 9835050478 1297718599
0847076219 7460588742 3256995828 8925350419 3795826061 6211842368 7685114183 1606831586
7994601652 0577405294 2305360178 0313357263 2670547903 3840125730 5912339601 8801378254
2192709476 7337191987 2873852480 5742124892 1183470876 6296672072 7232565056 5129333126
0595057777 2754247124 1648312832 9820723617 5057467387 0128209575 5443059683 9555568686
1188397135 5220844528 5264008125 2027665557 6774959696 2661260456 5245684086 1392382657
6858338469 8499778726 7065551918 5446869846 9478495734 6226062942 1962455708 5371272776
5230989554 5019303773 2166649182 5781546772 9200521266 7143463209 6378918523 2321501897
6126034373 6840671941 9303774688 0999296877 5824410478 7812326625 3181845960 4538535438
3911449677 5312864260 9252115376 7325886672 2604042523 4910870269 5809964759 5805794663
9734190640 1003636190 4042033113 5793365424 2630356145 7009011244 8008900208 0147805660
3710154122 3288914657 2239314507 6071670643 5568274377 4396578906 7972687438 4730763464
5167756210 3098604092 7170909512 8086309029 7385044527 1828927496 8921210667 0081648583
3955377359 1913695015 3162018908 8874842107 9870689911 4804669270 6509407620 4650277252
8650728905 3285485614 3316081269 3005693785 4178610969 6920253886 5034577183 1766868859
2368148847 5276498468 8219497397 2970773718 7188400414 3231276365 0481453112 2850990020
7424092558 5925292610 3021067368 1543470152 5234878635 1643976235 8604191941 2969769040
5264832347 0099111542 4260127343 8022089331 0966863678 9869497799 4001260164 2276092608
2349304118 0643829138 3473546797 2539926233 8791582998 4864592717 3405922562 0749105308
5315371829 1168163721 9395188700 9577881815 8685046450 7699343940 9874335144 3162633031
7247747486 8979182092 3948083314 3970840673 0840795893 5810896656 4775859905 5637695252
3265361442 4780230826 8118310377 3588708924 0613031336 4773710116 2821461466 1679404090
5186152603 6009252194 7218890918 1073358719 6414214447 8654899528 5823439470 5007983038
8538860831 0357193060 0277119455 8021911942 8999227223 5345870756 6246926177 6631788551
4435021828 7026685610 6650035310 5021631820 6017609217 9846849368 6316129372 7951873078
9726373537 1715025637 8733579771 8081848784 5886650433 5824377004 1477104149 3492743845
7587107159 7315594394 2641257027 0965125108 1155482479 3940359768 1188117282 4721582501
0949609662 5393395380 9221955919 1818855267 8062149923 1727631632 1833989693 8075616855
9117529984 5013206712 9392404144 5938623988 0938124045 2191484831 6462101473 8918251010
9096773869 0664041589 7361047643 6500068077 1056567184 8628149637 1118832192 4456639458
1449148616 5500495676 9826903089 1118568798 6929470513 5248160917 4324301538 3684707292
8989828460 2223730145 2655679898 6277679680 9146979837 8268764311 5988321090 4371561129
9766521539 6354644208 6919756737 0005738764 9784376862 8768179249 7469438427 4652563163
2300555130 4174227341 6464551278 1278457777 2457520386 5437542828 2567141288 5834544435
1325620544 6424101103 7955464190 5811686230 5964476958 7054072141 9852121067 3433241075
6767575818 4569906930 4604752277 0167005684 5439692340 4171108988 8993416350 5851578873
5343081552 0811772071 8803791040 4698306957 8685473937 6564336319 7978680367 1873079693
9242363214 4845035477 6315670255 3900654231 1792015346 4977929066 2415083288 5839529054
2637687668 9688050333 1722780018 5885069736 2324038947 0047189761 9347344308 4374437599
2503417880 7972235859 1342458131 4404984770 1732361694 7197657153 5319775499 7162785663
1190469126 0918259124 9890367654 1769799036 2375528652 6375733763 5269693443 5440047306
7198868901 9681474287 6779086697 9688522501 6369498567 3021752313 2529265375 8964151714
7955953878 4278499866 4563028788 3196209983 0494519874 3963690706 8276265748 5810439112
2326187940 5994155406 3270131989 8957037611 0532360629 8674803779 1537675115 8304320849
8720920280 9297526498 1256916342 5000522908 8726469252 8466610466 5392171482 0801305022
9805263783 6426959733 7070539227 8915351056 8883938113 2497570713 3102950443 0346715989
4487868471 1643832805 0692507766 2745001220 0352620370 9466023414 6489983902 5258883014
8678162196 7751945831 6771876275 7200505439 7944124599 0077115205 1546199305 0983869825
4284640725 5540927403 1325716326 4079293418 3342147090 4125425335 2324802193 2277075355
5467958716 3835875018 1593387174 2360615511 7101312352 5633485820 3651461418 7004920570
4372018261 7331947157 0086757853 9336078622 7395581857 9758725874 4102542077 1054753612
9404746010 0094095444 9596628814 8691590389 9071865980 5636171376 9222729076 4197755177
7201042764 9694961105 6220592502 4202177042 6962215495 8726453989 2276976603 1052498085
5759471631 0758701332 0886146326 6412591148 6338812202 8444069416 9488261529 5776253250
1987035987 0674380469 8219420563 8125583343 6421949232 2759372212 8905642094 3082352544
0841108645 4536940496 9271494003 3197828613 1818618881 1118408257 8659287574 2638445005
9944229568 5864604810 3301538891 1499486935 4360302218 1094346676 4000022362 5505736312
9462629609 6198760564 2599639461 3869233083 7196265954 7392346241 3459779574 8524647837
9807956931 9865081597 7675350553 9189911513 3525229873 6112779182 7485420086 8953965835
9421963331 5028695611 9201229888 9887006079 9927954111 8826902307 8913107603 6176347794
8943203210 2773359416 9086500719 3280401716 3840644987 8717537567 8118532132 8408216571
1075495282 9497493621 4608215583 2056872321 8557406516 1096274874 3750980922 3021160998
2633033915 4694946444 9100451528 0925089745 0748967603 2409076898 3652940657 9201983152
6541065813 6823791984 0906457124 6894847020 9357761193 1399802468 1340520039 4781949866
2026240089 0215016616 3813538381 5150377350 2296607462 7952910384 0686855690 7015751662
4192987244 4827194293 3100485482 4454580718 8976330032 3252582158 1280327467 9620028147
6243182862 2171054352 8983482082 7345168018 6131719593 3247110746 6222850871 0666117703
4653528395 7762599774 4672185715 8161264111 4327179434 7885990892 8084866949 1413909771
6736900277 7585026866 4654056595 0394867841 1107901161 0400857274 4562938425 4941675946
0548711723 5946429105 8509099502 1495879311 2196135908 3158826206 8233215615 3086833730
8381732793 2819698387 5087083483 8804638847 8441884003 1847126974 5437093732 9836240287
5197920802 3218787448 8287284372 7378017827 0080587824 1074935751 4889978911 7397461293
2035108143 2703251409 0304874622 6294234432 7571260086 6425083331 8768865075 6429271605
5252895449 2153765175 1492196367 1810494353 1785838345 3865255656 6406572513 6357506435
3236508936 7904317025 9787817719 0314867963 8408288102 0946149007 9715137717 0990619549
6964007086 7667102330 0486726314 7551053723 1757114322 3174114116 8062286420 6388906210
1923552235 4671166213 7499693269 3217370431 0598722503 9456574924 6169782609 7025335947
5020913836 6737728944 3869640002 8110344026 0847128990 0074680776 4844088711 3413525033
6787731679 7709372778 6821661178 6534423173 2264637847 6978751443 3209534000 1650692130
5464768909 8505020301 5044880834 2618452087 3053097318 9492916425 3229336124 3151430657
8264070283 8984098416 0295030924 1897120971 6016492656 1341343342 2298827909 9217860426
7981245728 5345801338 2609958771 7811310216 7340256562 7440072968 3406619848 0676615805
0216918337 2368039902 7931606420 4368120799 0031626444 9146190219 4582296909 9212278855
3948783538 3056468648 8165556229 4315673128 2743908264 5061162894 2803501661 3366978240
5177015521 9626522725 4558507386 4058529983 0379180350 4328767038 0925216790 7571204061
2375963276 8567484507 9151147313 4400018325 7034492090 9712435809 4479004624 9431345502
8900680648 7042935340 3743603262 5820535790 1183956490 8935434510 1342969617 5452495739
6062149028 8728932792 5206965353 8639644322 5388327522 4996059869 7475988232 9916263545
9733244451 6375533437 7492928990 5811757863 5555562693 7426910947 1170021654 1171821975
0519831787 1371060510 6379555858 8905568852 8879890847 5091576463 9074693619 8815078146
8526213325 2473837651 1929901561 0918977792 2008705793 3964638274 9068069876 9168197492
3656242260 8715417610 0430608904 3779766785 1966189140 4144925270 4808819714 9880154205
7787006521 5940092897 7760133075 6847966992 9554336561 3984773806 0394368895 8876460549
8387147896 8482805384 7017308711 1776115966 3505039979 3438693391 1978988710 9156541709
1330826076 4740630571 1411098839 3880954814 3782847452 8838368079 4188843426 6622207043
8722887413 9478010177 2139228191 1992365405 5163958934 7426395382 4829609036 9002883593
2774585506 0801317988 4071624465 6399794827 5783650195 5142215513 3928197822 6984278638
3916797150 9126241054 8725700924 0700454884 8569295044 8110738087 9965474815 6891393538
0943474556 9721289198 2717702076 6613602489 5814681191 3361412125 8783895577 3571949863
1721084439 8901423948 4966592517 3138817160 2663261931 0653665350 4147307080 4414939169
3632623737 6777709585 0313255990 0957627319 5730864804 2467701212 3270205337 4266705314
2448208168 1303063973 7873664248 3672539837 4876909806 0218278578 6216512738 5635132901
4890350988 3270617258 9325753639 9397905572 9175160097 6154590447 7169226580 6315111028
0384360173 7474215247 6085152099 0161585823 1257159073 3421736576 2671423904 7827958728
1505095633 0928026684 5893764964 9770232973 6413190609 8274063353 1089792464 2421345837
4090116939 1964250459 1288134034 9881063540 0887596820 0544083643 8651661788 0557608956
8967275315 3808194207 7332597917 2784376256 6118431989 1025007491 8290864751 4979400316
0703845549 4653859460 2745244746 6812314687 9434416109 9333890899 2638411847 4252570445
7251745932 5738989565 1857165759 6148126602 0310797628 2541655905 0604247911 4016957900
3383565748 6925280074 3025623419 4982864679 1447632277 4005529460 9039401775 3633565547
1931000175 4300475047 1914489984 1040015867 9461792416 1001645471 6551337074 0739502604
4276953855 3834397550 5488710997 8520540117 5169747581 3449260794 3368954378 3221172450
6873442319 8987884412 8542064742 8097356258 0706698310 6979935260 6933921356 8588139121
4807354728 4632277849 0808700246 7776303605 5512323866 5629517885 3719673034 6347012229
3958160679 2509153217 4890308408 8651606111 9011498443 4123501246 4692802880 5996134283
5118847154 4977127847 3361766285 0621697787 1774382436 2565711779 4500644777 1837022199
9106695021 6567576440 4499794076 5037999954 8450027106 6598781360 3802314126 8369057831
9046079276 5297277694 0436130230 5178708054 6511542469 3952651271 0105292707 0306673024
4471259739 3995051462 8404767431 3637399782 5918454117 6413327906 4606365841 5292701903
0276017339 4748669603 4869497654 1752429306 0407270050 5903950314 8522921392 5755948450
7886797792 5253931765 1564161971 6844352436 9794447355 9642606333 9105512682 6061595726
2170366985 0647328126 6724521989 0605498802 8078288142 9796336696 7441248059 8219214633
9565745722 1022986775 9974673812 6069367069 1340815594 1201611596 0190237753 5255563006
0624798326 1249881288 1929373434 7686268921 9239777833 9107331065 8825681377 7172328315
3290825250 9273304785 0724977139 4483338925 5208117560 8452966590 5539409655 6854170600
1179857293 8139982583 1929367910 0391844099 2865756059 9359891000 2969864460 9747147184
7010153128 3762631146 7742091455 7404181590 8800064943 2378558393 0853082830 5476076799
5243573916 3122188605 7549673832 2431956506 5546085288 1201902363 6447127037 4863442172
7257879503 4284863129 4491631847 5347531435 0413920961 0879605773 0987201352 4840750576
3719925365 0470908582 5139368634 6386336804 2891767107 6021111598 2887553994 0120076013
9470336617 9371539630 6139863655 4922137415 9790511908 3588290097 6566473007 3387931467
8913181465 1093167615 7582135142 4860442292 4453041131 6065270097 4330088499 0346754055
1864067734 2603583409 6086055337 4736276093 5658853109 7609942383 4738222208 7292464497
6845605795 6251676557 4088410321 7313456277 3585605235 8236389532 0385340248 4227337163
9123973215 9954408284 2166663602 3296545694 7035771848 7344203422 7706653837 3875061692
1276801576 6181095420 0977083636 0436111059 2409117889 5403380214 2652394892 9686439808
9261146354 1457153519 4342850721 3534530183 1587562827 5733898268 8985235577 9929572764
5229391567 4775666760 5108788764 8453493636 0682780505 6462281359 8885879259 9409464460
4170520447 0046315137 9754317371 8775603981 5962647501 4109066588 6616218003 8266989961
9655805872 0863972117 6995219466 7898570117 9833244060 1811575658 0742841829 1061519391
7630059194 3144346051 5404771057 0054339000 1824531177 3371895585 7603607182 8605063564
7997900413 9761808955 3636696031 6219311325 0223851791 6720551806 5926351803 6251214575
9262383693 4822266589 5576994660 4919381124 8660909979 8128571823 4940066155 5219611220
7203092277 6462009993 1524427358 9488710576 6238946938 8944649509 3960330454 3408421024
6240104872 3328750081 7491798755 4387938738 1439894238 0117627008 3719605309 4383940063
7561164585 6094312951 7597713935 3960743227 9248922126 7045808183 3137641658 1826956210
5872892447 7400359470 0926866265 9651422050 6300785920 0248829186 0839743732 3538490839
6432614700 0532423540 6470420894 9921025040 4726781059 0836440074 6638002087 0126664209
4571817029 4675227854 0074508552 3777208905 8168391844 6592829417 0182882330 1497155423
5235911774 8186285929 6760504820 3864343108 7795628929 2540563894 6621948268 7110428281
6389397571 1757786915 4301650586 0296521745 9581988878 6804081103 2843273986 7198621306
2055598552 6603640504 6282152306 1545944744 8990883908 1999738747 4529698107 7620148713
4000122535 5222466954 0931521311 5337915798 0269795557 1050850747 3874750758 0687653764
4578252443 2638046143 0428892359 3485296105 8269382103 4980004052 4840708440 3561167817
1705128133 7880570564 3450616119 3304244407 9826037795 1198548694 5591520519 6009304127
1007277849 3015550388 9536033826 1929343797 0818743209 4991415959 3396368110 6275572952
7800425486 3060054523 8391510689 9891357882 0019411786 5356821491 1852820785 2130125518
5184937115 0342215954 2244511900 2073935396 2740020811 0465530207 9328672547 4054365271
7595893500 7163360763 2161472581 5407642053 0200453401 8357233829 2661915308 3540951202
2632916505 4426123619 1970516138 3935732669 3760156914 4299449437 4485680977 5696303129
5887191611 2929468188 4936338647 3927476012 2696415884 8900965717 0861605981 4720446742
8664208765 3347998582 2209061980 2173211614 2304194777 5499073873 8567941189 8246609130
9169177227 4207233367 6350326783 4058630193 0193242996 3972044451 7928812285 4478211953
5308989101 2534297552 4727635730 2262813820 9180743974 8671453590 7786335301 6082155991
1314144205 0914472935 3502223081 7193663509 3468658586 5631485557 5862447818 6201087118
8976065296 9899269328 1787055764 3514338206 0141077329 2610634315 2533718224 3385263520
2177354407 1528189813 7698755157 5745469397 2715048846 9793619500 4777209705 6179391382
8989845327 4262272886 4710888327 0173723258 8182446584 3624958059 2560338105 2156062061
5571329915 6084892064 3403033952 6226345145 4283678698 2880742514 2256745180 6184149564
6861116354 0497189768 2154227722 4794740335 7152743681 9409892050 1136534001 2384671429
6551867344 1537416150 4256325671 3430247655 1252192180 3578016924 0326699541 7460875924
0920700466 9340396510 1781348578 3569444076 0470232540 7555577647 2845075182 6890418293
9661133101 6013111907 7398632462 7782190236 5066037404 1606724962 4901374332 1724645409
7412995570 5291424382 0807609836 4823465973 8866913499 1978401310 8015581343 9791948528
3043673901 2482082444 8141280954 4377389832 0059864909 1595053228 5791457688 4962578665
8859991798 6752055455 8099004556 4611787552 4937012455 3217170194 2828846174 0273664997
8475508294 2280202329 0122163010 2309772151 5694464279 0980219082 6689868834 2630716092
0791408519 7695235553 4886577434 2527753119 7247430873 0436195113 9611908003 0255878387
6442060850 4473063129 9277888942 7291897271 6989057592 5244679660 1897074829 6094919064
8764693702 7507738664 3239191904 2254290235 3189233772 9316673608 6996228032 5571853089
1928440380 5071030064 7768478632 4319100022 3929785255 3723755662 1364474009 6760539439
8382357646 0699246526 0089090624 1059042154 5392790441 1529580345 3345002562 4410100635
9530039598 8644661695 9562635187 8060688513 7234627079 9732723313 4693971456 2855426154
6765063246 5676620279 2452085813 4771760852 1691340946 5203076733 9184114750 4140168924
1213198268 8156866456 1485380287 5393311602 3229255561 8941042995 3356400957 8649534093
5115266454 0244187759 4931693056 0448686420 8627572011 7231952640 5023099774 5676478384
8897346431 7215980626 7876718380 0524769688 4084989185 0861490034 3240347674 2686245952
3958903585 8213500645 0998178244 6360873177 5437885967 7672919526 1112138591 9472545140
0301180503 4378752776 6440276261 8941017576 8726804281 7662386068 0477885242 8874302591
4524707395 0546525135 3394595987 8961977891 1041890292 9438185672 0507096460 6263541732
9446495766 1265195349 5701860015 4126239622 8641389779 6733329070 5673769621 5649818450
6842263690 3678495559 7002607986 7996261019 0393312637 6855696876 7029295371 1625280055
4310078640 8728939225 7145124811 3577862766 4902425161 9902774710 9033593330 9304948380
5978566288 4478744146 9841499067 1237647895 8226329490 4679812089 9848571635 7108783119
1848630254 5016209298 0582920833 4813638405 4217200561 2198935366 9371336733 3924644161
2522319694 3471206417 3754912163 5700857369 4397305979 7097197266 6664226743 1117762176
4030686813 1035189911 2271339724 0368870009 9686292254 6465006385 2886203938 0050477827
6912835603 3725482557 9391298525 1506829969 1077542576 4748832534 1412132800 6267170940
0909822352 9657957997 8030182824 2849022147 0748111124 0186076134 1515038756 9830918652
7806588966 8236252393 7845272634 5304204188 0250844236 3190383318 3845505223 6799235775
2929106925 0432614469 5010986108 8899914658 5518818735 8252816430 2520939285 2580779697
3762084563 7482114433 9881627100 3170315133 4402309526 3519295886 8069082135 5853680161
0002137408 5115448491 2685841268 6958991741 4913382057 8492800698 2551957402 0181810564
1297250836 0703568510 5533178784 0829000041 5525118657 7945396331 7538532092 1497205266
0783126028 1961164858 0986845875 2512999740 4092797683 1766399146 5538610893 7587952214
9717317281 3151793290 4431121815 8710235187 4075722210 0123768721 9447472093 4931232410
7065080618 5623725267 3254073332 4875754482 9675734500 1932190219 9119960797 9893733836
7324257610 3938985349 2787774739 8050808001 5544764061 0535222023 2540944356 7718794565
4304067358 9649101761 0775948364 5408234861 3025471847 6485189575 8366743997 9150851285
8020607820 5544629917 2320202822 2914886959 3997299742 9747115537 1858924238 4938558585
9540743810 4882624648 7880533042 7146301194 1589896328 7926783273 2245610385 2197011130
4665871005 0008328517 7311776489 7352309266 6123458887 3102883515 6264460236 7199664455
4727608310 1187883891 5114934093 9344750073 0258558147 5619088139 8752357812 3313422798
6650352272 5367171230 7568610450 0454897036 0079569827 6263923441 0714658489 5780241408
1584052295 3693749971 0665594894 4592462866 1996355635 0652623405 3394391421 1127181069
1052290024 6574236041 3009369188 9255865784 6684612156 7955425660 5416005071 2766417660
5687427420 0329577160 6434486062 0123982169 8271723197 8268166282 4993871499 5449137302
0518436690 7672357740 0053932662 6227603236 5975171892 5901801104 2903842741 8550789488
7438832703 0632832799 6300720069 8012244365 1163940869 2222074532 0244624121 1558043545
4206421512 1585056896 1573564143 1306888344 3185280853 9759277344 3365538418 8340303517
8229462537 0201578215 7373265523 1857635540 9895403323 6382319219 8921711774 4946940367
8296185920 8034038675 7583411151 8824177439 1450773663 8407188048 9358256868 5420116450
3135763335 5509440319 2367203486 5101056104 9872726472 1319865434 3545040913 1859513145
1812764373 1043897250 7004981987 0521762724 9406521461 9959232142 3144397765 4670835171
4749367986 1865527917 1582408065 1063799500 1842959387 9915835017 1580759883 7849622573
9851212981 0326379376 2183224565 9423668537 6799113140 1080431397 3233544909 0824910499
1433258432 9882103398 4698141715 7560108297 0658306521 1347076803 6806953229 7199059990
4451209087 2757762253 5104090239 2888779424 6304832803 1913271049 5478599180 1969678353
2146444118 9260631526 6181674431 9355081708 1875477050 8026540252 9410921826 4858213857
5266881555 8411319856 0022135158 8872103656 9608751506 3187533002 9421186822 2189377554
6027227291 2905042922 5978771066 7873840000 6167721546 3844129237 1193521828 4998243509
2089180168 5572798156 4218581911 9749098573 0570332667 6464607287 5743056537 2602768982
3732597450 8447964954 5648030771 5981539558 2777913937 3601717422 9960273531 0276871944
9444917939 7851446315 9731443535 1850491413 9415573293 8204854212 3508173912 5497498193
0871439661 5132942045 9193801062 3142177419 9184060180 3479498876 9105155790 5554806953
8785400664 5337598186 2846419905 2204528033 0626369562 6490910827 6271159038 5699505124
6529996062 8554438383 3032763859 9800792922 8466595035 5121124528 4087516229 0602620118
5777531374 7949362055 4964010730 0134885315 0735487353 9056029089 3352640071 3274732621
9603117734 3394367338 5759124508 1493357369 1166454128 1788171454 0230547506 6713651825
8284898099 5121391939 9563324133 6556777098 0030819102 7204099714 8687418134 6670060940
5102146269 0280449159 6465453301 0775469541 3088714165 3125448130 6119240782 1188690056
0277818242 3502269618 9344352547 6335735364 8561936325 4417756613 9817039306 3287216690
5722259745 2091929172 6219984440 9646158269 4563802395 0283712168 6446561785 2355651641
2771282691 8688615572 7162014749 3405227694 6595712198 3149433816 2211400693 6307430444
1732847861 0177774383 7977037231 7952554341 0722344551 2555589998 6461838767 6490397246
1167959018 1000350989 2864120419 5163551108 7632042676 1297982652 9425882951 1412758412
6273279079 8807559751 8515768412 6474220947 9721843309 3529726652 1001566251 4552994745
1276315509 1763673025 9462132930 1904028379 5424632325 8550301096 7069227202 2707486341
9005438302 6506812141 4213505715 4175057508 6399076739 4633514620 9082888934 9383764393
9925690060 4067311422 0933121959 3620298297 2351163259 3867722414 7791162957 2780752395
0562515816 0313335938 2311500518 6268905306 5836812998 8108663263 2719806112 7154885879
8093487912 9137074982 3057592909 1862939195 0147211975 8606727009 2547718025 7503377307
9939713453 9532646195 2699965963 8565491759 0458333585 7991020127 1320458390 3200853878
8816336376 8518208372 7885131175 2277696097 8796214237 2162545214 5912818317 9821604411
1311671406 9148271709 8101545778 1939202311 5638719508 0502467972 5792497605 7726259133
2855972637 1211201905 7207714091 4864507409 4926718035 8151575715 1405039761 0963846755
5692989703 8354731410 0223802583 4687673501 2977541327 9532060971 1545064842 1218593649
0997917766 8747744818 8287063231 5515865032 8981642282 8823274686 6106592732 1979071623
8464215348 9852476216 7890502609 9804526648 3929542357 2873439776 8049577409 1449538391
5755654854 5905897649 5198513801 0079580107 8375994577 5299196700 5476022525 5203445398
8712538780 1719607181 6407812484 7847257912 4078245443 6168234523 9570689514 2722697504
3187363326 3011103053 4233358216 0933319121 8806608268 3414289104 1517324721 6053355849
9932245487 3077882290 5252324234 8615315209 7693846104 2582849714 9634753418 3756200301
4915703279 6853018686 3157248840 1526639835 6895636346 5743532178 3493199825 5421173084
6774529708 5839507616 4582296303 2442432823 7737450517 0285606980 6788952176 8198156710
7816334052 6675953942 4926280756 9683261074 9532339053 6223090807 0814559198 3735537774
8742029039 0181429373 1152933464 4468151212 9450975965 3430628421 5319445727 1186149000
1765055817 7095302468 8752632501 1970520947 6159416768 7277844720 0019278913 7251841622
8577837922 8443908430 1181121496 3664246590 3363419454 0657183544 7719124466 2125939265
6620306888 5200555991 2123536371 8226922531 7814587925 9375044144 8933981608 6579008761
6502463519 7045828895 4817937566 8104647461 4105142498 8702521399 3687050937 2305447734
1126413548 9280684105 9107716677 8212383328 1026218558 7751312721 1793444482 0144042574
5083063944 7383637939 0628300897 3306241380 6145894142 2769474793 1665717623 1824721683
5067807648 7573420491 5576282175 8397297513 4478990696 5895325489 4033561561 3167403276
4724692125 0575911625 1529654568 5446334981 1431767025 7295661844 7754874693 7846423373
7238981920 6620485118 9437886822 4807279352 0225017965 4534375727 4163910791 9729529508
1294292220 5347717304 1844779156 7399173841 8311710362 5243957161 5271466900 5814700002
6330104526 4354786590 3290733205 4683388720 7873544476 2647925297 6901709120 0787418373
6735087713 3769776834 9634425241 9949951388 3150748775 3743384945 8259765560 9965559543
1804092017 8497184685 4973706962 1208852437 7013853757 6814166327 2241263442 3982152941
6453780004 9250726276 5150789085 0712659970 3670872669 2764308377 2296859851 6912230503
7462744310 8529343052 7307886528 3977335246 0174635277 0320593817 9125396915 6210636376
2588293757 1373840754 4064689647 8310070458 0613446731 2715911946 0843593582 5987782835
2665311510 6504162329 5329047772 1740835593 4972375855 2138048305 0900096466 7608830154
0612824308 7406455944 3185341375 5220166305 8121110334 5312074508 6824339432 1590435944
3031243122 7471385842 0303901060 7094031523 5556172767 9941600203 9397509989 7629335325
8555756248 0899669182 9864222677 5023601932 5797472674 2578211119 7347094023 5745722227
1212526852 3842958742 7350156366 0093188045 4933389897 4157149054 4182559738 0808715652
8143010267 0460284316 8192303925 3529779576 5862414392 7015497408 7927313105 1636119137
5770089295 6482332364 8298263024 6079758757 6774537716 0102490804 6243018565 2416175665
5600160859 1215345562 6760219268 9982855377 8725831451 4408265458 3484409478 4631787773
7479465358 0169960779 4055687011 9232860804 1130904629 3508718271 2593466871 2766694873
8998245985 2778649956 9165464029 4589350649 6433580982 4765965165 1420909867 5520380830
9203230487 3427034682 8875160407 1546653834 6196112230 1375945157 9252696743 6425319273
9003603860 8236450762 6988274976 1872357547 6762889950 7521148048 5252795084 5033958570
8381304769 3788132112 3674281319 4879502280 6632017002 2460331989 6719706491 6374117585
4851878484 0120548446 7258885140 1562725019 8217190669 6081262778 5485964818 3696214107
2171421498 6361918774 7545096503 0895709947 0934337856 9816744658 2826791194 0611956037
8453978558 3924076127 6344105766 7510243075 5981455278 6167815949 6570625597 5507430652
1085301597 9080733437 3607943286 6757890533 4836695554 8680391343 3720156498 8342208933
9997164147 9746938696 9054800891 9306713805 7171505857 3071488156 4992071408 6758259602
8760564597 8242377024 2469805328 0566327870 4192676846 7116266879 4634869504 6450742021
9373945259 2626686135 5294062478 1361206202 6364981999 9949840514 3868285258 9563422643
2870766329 9304891723 4007254717 6418868535 1372332667 8779217383 4754148002 2803392997
3579361524 1275582956 9276837231 2347989894 4627433045 4566790062 0324205163 9628258844
3085438307 2014956721 0646053323 8537203143 2421126074 2448584509 4580494081 8209276391
4000854042 2023556260 2185643489 9414543995 0410980591 8179488826 2805206644 1086319001
6885681551 6922948620 3010738897 1810077092 9059048074 9092427141 0189335428 1842999598
8169660993 8369616443 8152887721 4085268088 7574882932 5873580990 5670755817 0179491619
0611400190 8553744882 7262009366 8560447559 6557476485 6740081773 8170330738 0305476973
6097865438 5938218722 0583902344 4435088674 9986650604 0645874346 0053318274 3629617786
2518081893 1443632512 0510709469 0813586440 5192295129 3245007883 3398788429 3393424351
2634336520 4385812912 8343452973 0865290978 3300671261 7981303167 9438553572 6296998740
3595704584 5223085639 0098913179 4759487521 2639707837 5944861139 4519602867 5121056163
8976008880 0927461158 6080020780 3341591451 7970730368 3519697776 6076373785 3330120241
2011204698 8609209339 0853657732 2239

Editor's note: Pi to 100 million decimal places

Pi is a programming (better a specification) language. It was developed in 1984 and is used at some German universities (for example at University of Potsdam).
It was made to develop specifications. Specifcations are provisional programs. They are not for making real programs which can be shipped, but to formulate a given problem into an algorithm, implement this algorithm, test it and show it to client to verify, that that is what he wanted. Then you can start making the real program basing on this specification.
The given Pi-Compiler (can be downloaded from http://www.cs.uni-potsdam.de/~owilhelm/Manuskripte/Pi/pi.zip ) translates the given specification into Haskell (in fact the compiler is buggy so there is a pre-compiler which translates the given code, so that the compiler understands it and a post-compiler, so that the Haskell-code is working).

How to write a Pi-specification (please make yourself familiar with specifications before reading the following):
As stated in specification it consists of the export, the import, the common parameters and the body. In the first three there are only the signatures of the operations and types ( in import and common parameters are these which are not in this module (specification) ). A signature is the first line of an operation (ex. in C int add (int x, int y) ).
To show you how this all works I show you a short specification of the natural numbers + 0 ({0,1,...}):

this is what is exported.

```cem NAT
type view specification

export

type Nat

constructor null : -> Nat
constructor successor: Nat -> Nat
operation null : -> Nat
operation successor: Nat -> Nat
operation add : Nat,Nat -> Nat
operation one : -> Nat
operation two : -> Nat
```

The import is empty as we only import one specification, but this is also needed to be exported
```import
```

```common parameters
type Logic
operation true : -> Logic
operation false : -> Logic
constructor true : -> Logic
constructor false : -> Logic
```

Now the body
```body
construction of type Nat is internal
constructor null : -> Nat
constructor successor: Nat -> Nat

operation add : Nat,Nat -> Nat
variables x,y : Nat
equations

operation one : -> Nat
equations one = successor(null)

operation two : -> Nat
equations two = successor(one)
```

A constructor is the basis on which a type is constructed.

Please Note: Most of the modules are German so it can be hard for non-german speakers to understand

The world's longest mnemonic for pi is a short story by Michael Keith entitled Cadaeic Cadenza. This record was previously held by Poe, E., Near a Raven (encoding the first 740 digits of pi) by the same author.

Cadaeic Cadenza encodes the first 3835 digits of pi, while simultaneously being an interesting read -- not a simple feat.

I think I should elaborate on what others have said about solving for pi. You can approximate pi/4 as accurately as your heart desires by the formula 1 - 1/3 + 1/5 - 1/7 + 1/9 ... always alternating adding and subtracting, and adding two to the denominator. Note that when you are on the adding phase you will always be slightly above pi/4, and on the subtracting phase you will always be just a little below pi/4. But if you just decide how many digits you need pi to, you can run the equation until the digits you will actually use stop changing, and are therefor accurate. Then multiply your result by 4 (because remember, this is solving for pi/4) and ta-da, pi. Here look, I wrote this C++ program to find pi:

```#include "iostream.h"

int main(int argc, char* argv)
{
long double pi=1;
int denominator = 3;
bool alt = 0;
long double divisor;

while (true)
{
divisor = 1 / (long double)denominator;
cout << pi*4 << " ";

if (alt == 0)
{
pi = pi - divisor;
alt = 1;
}
else
{
pi = pi + divisor;
alt = 0;
}

denominator += 2;
}
return 0;
}```

I'm no expert coder, so there is probably a way to get more digits in the output that I'm to stupid to know about, I'll update here and say so if I ever figure it out. -grin- But in the mean time, play with that.

Pi

~Wislawa Szymborska~

Three point one four one.
All the following digits are also initial,
Five nine two because it never ends.
It can't be comprehended six five three five at a glance,
Eight nine by calculation,
Seven nine or imagination,
Not even three two three eight by wit, that is, by comparison
Four six to anything else
Two six four three in the world.
The longest snake on earth calls it quits at about forty feet.
Likewise, snakes of myth and legend, though they may hold out a bit longer.
The pageant of digits comprising the number pi
Doesn't stop at the page's edge.
It goes on across the table, through the air,
Over a wall, a leaf, a bird's nest, clouds, straight into the sky,
Through all the bottomless, bloated heavens.
Oh how brief - a mouse tail, a pigtail - is the tail of a comet!
How feeble the star's ray, bent by bumping up against space!
While here we have two three fifteen three hundred nineteen
My phone number your shirt size the year
Nineteen hundred and seventy-three the sixth floor
The number of inhabitants sixty-five cents
Hip measurement two fingers a charade, a code,
In which we find hail to thee, blithe spirit, bird thou never wert
Alongside ladies and gentlemen, no cause for alarm,
As well as heaven and earth shall pass away,
But not the number pi, oh no, nothing doing,
It keeps right on with its rather remarkable five,
Its uncommonly fine eight,
Its far from final seven,
Nudging, always nudging a sluggish eternity
To continue.
starting with the following function:
```f(x)= -1     x < 0
= 0      x = 0
= 1      x > 0
```
notice that f(x) is odd and as such, it's fourier series expansion will only have sin() coeficients:
```     +inf
f(x)= Σ an * sin(2*n*Pi*x/L)
n=1
```
where

an - fourier series coeficients yet to be determined
L - length of the interval

an (the fourier series coeficients) are calculated as:

an=2/L * integral(a, a+L, f(x)*sin(2*n*pi*x/L), x)

if we calculate the expansion from a=-1 to a+L=1 we get (L=2):

an=2/2*integral(-1,1,f(x)*sin(2*n*pi*x), x)

noticing that f(x) and sin() are odd functions, their product will be even, and as such we can say that

integral(-1,1, ..., x)=2*integral(0,1, ..., x)

then:

an =2*integral(-1,1,f(x)*sin(2*n*pi*x), x)
```   = 2/(n*pi) * (1-(-1)^n)
= 0           n even
4/(n*pi)    n odd
```

f(x) then becomes:
```      +inf
f(x) = Σ 2/(n*pi) * (1-(-1)^n) * sin(2*n*Pi*x/2)
n=1
```
changing variables n=2k+1 (getting rid of the even terms (which are 0)):
```      +inf
f(x) = Σ 4/((2k+1)*pi) * sin((2k+1)*Pi*x)
k=0
```
if we get the value of f(x)at x=1/2 (which we know to be 1):
```   +inf
1 = Σ 4/((2k+1)*pi) * sin(k*pi+Pi/2)
k=0

+inf
= Σ 4/((2k+1)*pi) * (-1)^k
k=0
```
divide by 4/pi:
```      +inf
pi/4 = Σ (-1)^k/(2k+1)
k=0

= 1 - 1/3 + 1/5 - 1/7 + ....
```
just thought it'd be interesting to know how to actually get the result.

note though that this converges very slowly. Check the pi metanode for faster ways of calculating pi.
Here's yet another way to derive pi:

Set xo to 2*sqrt(3).
Set yo to 3.

Define xn as:

2 * xn-1 * yn-1
xn-1 + yn-1

Define yn as sqrt(xn * yn-1).

The limit for both xn and yn as n approaches infinity will be pi.

When working with vectors, Π (uppercase) is also often used as a symbol for a plane.

For example:

`Π: r.(4 5 1) = 7`

is the equation of the plane Π

In number theory, the function pi(x) is defined to be the number of primes less than or equal to x. For example, pi(3)=2 since 2 and 3 are prime.

There have been many attempts to approximate the value of pi(x) for any given x. The logarithmic integral is one approximation of pi(x); indeed, in the limit (as x approaches infinity), the ratio pi(x)/Li(x) approaches one. This is one of the underlying results of the prime number theorem. Another famous approximation is given by Riemann and is based the logarithmic integral and the Mobius numbers:

```  ∞
-----
\
\    u(n)    /  1/n \
/   -----*li | x    |
/      n      \      /
-----
n=1
```

Where u(n) is the nth Mobius number. For most values of x, Riemann's estimate is among the best. But, whenever Li(x)<pi(x) (see Skewes number), Riemann's estimate is worse than many others.

For related information, see the Node of Prime, prime number and the Riemann zeta function. Note that since there are an infinite number of primes, pi(x) returns the value of every natural number at least once.

According to http://mathworld.wolfram.com/PrimeCountingFunction.html, the upper bound for pi(x) is (2x-6)/ln(x), where ln(x) is the natural logarithm of x.

An interesting point: To the best scientific guesses we have, the Universe .. Everything, ;-) .. shouldn't be more than a few Googol (10^100) kilometers wide, and it's probably a sphere or hypersphere. So you would use Pi to calculate its area or how much stuff is inside of it.

The thing is that to calculate anything to a Googol with significant digits, you only need 100 digits of Pi. So we could calculate the number of quarks (small atomic particles) in the entire Universe with, giving ourselves a thousand times more head-room than we think we need, 100,000 digits of Pi.

Here is the first 119,000 digits of Pi. Just imagine - with this number we could calculate perfectly the amount of atomic particles in Creation, if we had Its diameter (or some related precise measurement).

So, if this is the case, why do we have supercomputers working at this minute on Pi's digits well into the Billions? And why do people have it memorized to all those digits?

## π

Released in 1998. Written and directed by Darren Aronofsky. Rated R for language and disturbing imagery.

CAST:

Max believes that everything in life can be reduced to underlying patterns, or its basic math (kind of like Lawrence Waterhouse). His theory is as follows:

1. Mathematics is the language of nature;
2. Everything around us can be represented and understood by numbers;
3. If you graph these numbers, patterns emerge. Therefore: there are patterns everywhere in nature.

The project that he is currently working on is to find a pattern in the stock market. He has built a supercomputer called Euclid (a little in-joke, as Euclid, in Elements of Geometry, made certain observations that resulted in the discovery of π) to help him find this pattern.

Max's research with Euclid does not go unnoticed. A young woman named Marcy Dawson leaves cryptic messages on his answering machine, and arranges to bump into him "accidentally." She claims to be from a Wall Street firm that wants to hire him. While sitting in a diner, he meets a Hasidic Jew named Lenny Meyer, who tells him that the Torah is also numerical, and that people have been trying to find the underlying code of it as well.

As a result of these chance meetings, Max is a desirable commodity. This furthers his paranoia and heightens his stress, resulting in more migraines and hallucinations. At one point, he sees a human brain pulsing on the floor of a New York City subway car. It also drives his research. Unfortunately, Euclid keeps spitting out a 216 digit bug. This bug has been found before, by Sol. It is what caused his nervous breakdown. 216 is also believed, by Kabalists, to be the number of letters in the ultimate name of God. So everyone wants this number, which truly exists only in Max's mind.

Pi (?), n. [See Pica, Pie magpie, service-book.] (Print.)

A mass of type confusedly mixed or unsorted. [Written also pie.]

Pi, v. t. [imp. & p. p. Pied (?); p. pr. & vb. n. Pieing (?).] (Print.)

To put into a mixed and disordered condition, as type; to mix and disarrange the type of; as, to pi a form. [Written also pie.]

Pi (pI), n. [Gr. pi^.]

1.

A Greek letter (Π, π) corresponding to the Roman letter P.

2.

Specif.: (Math.) The letter Π, π, as used to denote the number or quotient approximately expressing the ratio of the circumference of a circle to its diameter; also, the quotient or the ratio itself. The value of the quotient pi, to eight decimal places, is 3.14159265. The quotient pi cannot be expressed as a root of an algebraic equation; and from this fact follows the impossibility of the quadrature of the circle by purely algebraic processes, or by the aid of a ruler and compass.

Log in or register to write something here or to contact authors.