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73,165,166,169,171,175,176,182,183,187,189,224,228,231,232,235)115.
FranciscusVieta(Fran,66-T,32,53,67,188,231-Te,67-)2,66-J3,66-ij2,67-,fi,67-e,32,67-e2,67Cooley,137,199Cooley-Tukeyalgarithm,199coprimalityandT,41,42Cotes,190coupledNewtoniteration,147Cox,95Crandall,230Cusanus,183,184Danielson,199DanteAlighieri,56,180,205dartboardalgorithm,39,40Dase,194,195,205DATAstatement,155Decerf,45definitionsofT,8Descartes,184,235Dichampt,206Dilcher,157division,145DNA,4Dodgson,seeCaroll46Dudley,8Duerer,181Ve,67e,11,14,25,32,37,60,6~84,85,116,189,190,202-seriesforspigotalgorithm,84emathematics,116e2,67educationalpoems,44-47Egypt,69,167,205,210elasticcurve,96,97Eratosthenes,38errordistributioncurve,10Escott,73,232Euclid,170euclidO,42Euclideanalgorithm,42Euler,10,11,13,64,70,74,97,100,166,186,188-190,194,224-226,230-232-formulae,224-226Euler'sfamous7rtheorem,14,61,190Euleriannumbers,157exhaustionmethod,169expmO,124exponentiation,binary,120,121Fagnano,97,98,234Felton,197,206Ferguson,50,205Fermat,6-LastTheorem,7Feynman,3Feynmanpoint,3,46FFTfastFouriertransform,137FFTmultiplication,16,137Fibonacci,75,180,205Fibonaccinumbers,75,234Filliatre,206Flammenkamp,37formulacollection7r,13-14,223-238FORTRAN,37,155,202Fourier,137Fox,39funnel,an(in)finite,164r(n),Euler'sGammafunction,226,234"f,Euler'sconstant,67Gardner,24Garwin,198Gauss,57,73,87,137,184,193,195,197,199,200,232,236-AGMalgorithm,90,91,102,114--derivative(Borwein),114--Schnhagevariant,93-and7r,87-102-errordistributioncurve,10Gauss-Legendremethod,87GaussJ.
GMO,93Genuys,197,206Girgensohn,48Gnaedinger,210Goldenratio,4>,60,66,68,76Goodwin,212Gosper,32,104,202,206,229Goto,47Greece,169Gregory,69,70,184,188-Series,70,189Grienberger,183,205Guilloud,206Haible,215Hardy,107,108,214Heath,257Hermann,232Hermite,196Index267hfloatlibrary,94,148,247-254high-performancealgorithms,16,198Hilbert,213HiramofTyre,169historicalnotes,209-214historyofdigitextractionrecords,207historyof7r,165-207historyof7rinthecomputerera,206historyof7rinthepre-computerera,205Hofstadter,15holytriangle,211Hutton,73,232Huygens,64,192hyperspheres,158Imhotep,211India,168,179,185,205individualdigitsof7r-anybase,128-hexadecimalbase,118Internet7rclubs,11Intuitionism,30IOCCC-InternationalObfuscatedCCodeContest,36irrationalityof7r,5,65,192jFunction,27Jacobi,95Japan,194Javaprogram-spigotalgorithmfor7r,77Jeans,44Jeenel,206Johnson,198Jones,165,193TheJoy0/7r,201Jugendforscht,63Jyesttha-devan,186Kabus,63,64Kanada,1,11,12,17,20,28,114,200,206Kanigel,105Karana-Paddhati,185Karatsuba,132268IndexKaratsubamultiplication,134Keith,45Kempermann,234Khintchine,68Khintchineconstant,68Kings,Bookof,169Klein,213Klingenstierna,73,232Knopp,228,233Knuth,28,120,121Koenig,199Kumbakonam,106Lagny,45,193,205,228Lagrange,95LamLay-Yong,176Lambert,5,65,192Lanczos,199Landau,10,213Lange,33,231Legendre,57,192Lehmann,205Leibniz,70,188,191,192,228-Series,70,157lemniscate,95-99LeonardodaVinci,181LeonardoofPisa(Fibonacci),75,180Levy,68library-hfioat,247-254Lievaart,37,85Lindemann,6,197LiuHui,177,183,205LiuXin,176Lone~73,106,232Lord,100LudolphvanCeulen,182,205Ludolphiannumber,153,183rn-zero,201Machin,13,72,73,166,192,205,232Machinformula,72Madhavan,186Maple(computeralgebrasystem),118Mapleprogram-LeibnizSeries,157Mathematica(computeralgebrasystem),35,111,118,127Matiyasevich,234Matsunaga,194,205Metius,181Miyoshi,206mnemonicverses,44-47modularequations,57,105moduloexponentiation,binary,120MonteCarlomethods,39Morgan,196multiplication,16,131-145,198-FFT,137-Karatsuba,132-schoolmethod,131-usingFouriertransforms,137-usinglogarithms,136MuPAD(computeralgebrasystem),118MuPADprogram-SqrtCoupledNewton,148-sumalt,151Nemorarius,184newgoals,19Newton,104,145,188,205,228Nicholson,206Nilakantha,186,205,223,224-formulae,223-224Niven,22Noether,213normalityof7r,4,21-34North,156nthrootcalculation,149NumberToCf0,66numericalintegrals,95numerology,25,154obfuscatedCseeIOCCC3601ds,65Osler,161,230Oughtred,166Parameswaran,186Peirce,14Percival,20,128,203,207performanceindexofarctanformulae,73Perron,65htm,77Plato,56,170,205Plouffe,19,47,48,60,117,128,207,227,235Poe,45Poeppe,210polygons,170,175positions,self-referential,3Preston,34,201primepairs,7Pringsheim,65probabilities,21probabilitysubjectivism,21Pschill,227PSQLalgorithm,118Ptolemy,176,205Rabinowitz,37,77,82radius,166radixconversion,79Ramanujan,13,27,57,58,104,105,199,200,214,226,227-biography,105-109-formulae,226-227-squaringthecirc1e,58Ramanujanand7r,103-111randomnumbergenerator,27,40randomnumbers,44randomnessof7r,21-34Regiomontanus,181Reitwiesner,206residualsum,186RhindPapyrus,167Rogers,65Romanus,182,205Rome,176roundingup,approximationthrough,38Rummler,162Runge,199Rtitherford,194,205Sadratnamala,185Sagan,14Index269Salamin,87,102,200,231,236Salomon,169Sastras,185Schnhage,92,236seriescalculation,150Shakespeare,46Shanks,D.
,49,62,197,206Shanks,W.
,50,195,205Sharp,189,205,228shortcutsto7r,35-50sieveprocedure,38SimonFraserUniversity,113Singmaster,213sliderule,136Smith,205Snell,50,178,183,205spigotalgorithm-fastervariant,82-pseudocode,80spigotalgorithms,77-85Spring,107squarerootcalculation,146squaringthecirc1e,7,170,181,196-withholes,162stateofpiart,1-20Stern,169,231Stieltjes,67Stifel,196Stirling,61,97,229Strassnitzky,194,232St(i)rmer,73,197,232,233Sulvasutras,168sumaltalgorithm,150symbol7r,165tables,239-245Takahashi,1,206Takebe,194,230Tamura,206TantaSangraham,185tertiumnondatur,30thetafunctions,95timeneededbyworldrecords,206transcendenceof7r,5,197Tropfke,169,171,180TsuChhung-Chih,5,178,205Thkey,137,198Umasvati,169270Indexuniverse,4,17,153Vega,193,205Viete,13,160-162,182,187,205Villegas,150VVagon,19,77,82,126,203,227VValdo,212VValker,107VVallis,9,64,161,163,187-product,9VVanMang,176VVangFan,177,205wavesinthe'Frsequence,34VVedeniwski,12VVells,190VVestley,35VVetherfield,232VVhish,185VViles,7VVilliams,26VVinter,37worldrecords,12-listof,205-207VVrenchJr.
,197,205,206,232VVVVVV,11Yoshino,206Yukti-Bhasa,185Yukti-Dipika,185Zagier,150zetafunction((s),234ZhangHeng,56,176,205Zinunermann,8Zoserpyramid,211ZuChongzhiseeTsuChhung-Chih178