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Bibliography Bibliography 1. Victor Adamchik, Stan Wagon, A Simple Formula lor 'Tr, American Mathe­ matical Monthly, Vol 104 (1997) 852-855, also in [20, pp. 557-559J. (Cited on p. 126) 2. Victor Adamchik, Stan Wagon, Pi: A 2000- Year Search Changes Direction, Education and Research, Vol 5 (1996), No. 1, 11-19, online at http://members . wri . com/victor/ articles/pi . html (Cited on p. 19, 126, 227) 3. Association pour le Developpement de la Culture Scientifique (ADCS), 61 rue Saint-Fuscien, 8000 Amiens France, Le nombre 'Tr, Sonderheft zur Zeitschrift Le PETIT ARCHIMEDE. 4. Timm Ahrendt, Schnelle Berechnung der komplexen Quadratwurzel aul hohe Genauigkeit, Logos Verlag, Berlin, 1996. Online at http://web.informatik.uni-bonn.de/II/staff/ahrendt/ AHRENDTliteratur.html (Cited on p. 148) 5. Gert Almquist, Many Correct Digits 01 'Tr, Revisited, American Mathematical Monthly, Vol. 104 (1997), No. 4, 351-353. (Cited on p. 157) 6. Archirnedes, Measurement 01 a Cirele, in The Works 01 Arehimedes, Ed. by T.L. Heath, Cambridge University Press, 1897, also in [20, pp. 7-14]. (Cited on p. 171) 7. Jörg Arndt, Remarks on arithmetical algorithms and the eompuation 01 'Tr, Online at http://www.jjj.de/joerg.html. (Cited on p. 75, 110, 233, 234) 8. Nigel Backhouse, Pancake lunctions and approximations to 'Tr. The Mathe­ matical Gazette, Vol. 79 (1995), 371-374. (Cited on p. 234) 9. David H. Bailey, The Computaion 01'Tr to 29,360,999 Decimal Digits Using Borweins' Quartically Convergent Algorithm, Mathematics of Computation, Vol. 50, No. 181 (Jan. 1988), 283-296, also in [20, pp. 562-575]. (Cited on p. 202) 10. David Bailey, Peter Borwein and Simon Plouffe, On The Rapid Computation 01 Various Polylogarithmie Constants, Online at http://ww . cecm. sfu. carpborwein, also in [20, pp. 663-676]. (Cited on p. 118, 123) 11. David H. Bailey, Jonathan M. Borwein and Peter B. Borwein, Ramanujan, Modular Equations, and Approximations to Pi or How to eompute One Billion Digits 01 Pi, American Mathematical Monthly, Vol. 96 (1989), 201-219, also in [20, pp. 623-641]. (Cited on p. 6, 105) 258 Bibliography 12. David H. Bailey, Jonathan M. Borwein and Richard E. Crandall, On the Khintchine Constant, Mathematics of Computation, Vol. 66, No. 217 (Jan. 1997),417-431. (Cited on p. 68) 13. David H. Bailey, Jonathan M. Borwein, Peter B. Borwein and Simon Plouffe, The Quest for Pi, The Mathematical Intelligencer, Vol. 19 (1997), No. 1, 50- 56. (Cited on p. 17, ll9, 122, 197, 200, 237, 238) 14. Walter William Rouse Ball, Mathematical Recreations and Essays, llth edi­ tion with revisions, Macmillan & Co Ltd, London, 1963. (Cited on p. 41, 180, 181, 182, 183) 15. Walter William Rouse Ball, Harold Scott Macdonald Coxeter, Mathematical Recreations and Essays, Toronto, 1974. (Cited on p. 25) 16. J. P. Ballantine, The best ('1) formula for computing 'Tr to a thousand places, American Mathematical Monthly, Vol. 46 (1939),499-501. (Cited on p. 74) 17. Friedrich L. Bauer, Decrypted Secrets, Methods and Maxims of Cryptology, Second, Revised and Extended Edition, Springer-Verlag, Heidelberg, 2000. (Cited on p. 61, 228) 18. Petr Beckmann, A History of'Tr (PI), Fifth Edition, The Golem Press, Boul­ der, Colorado, 1982. (Cited on p. 64, 188, 194, 195) 19. Fabrice Bellard, Computation of the n'th digit of pi on any base in O(n2 ), OnIine at http://www-stud . enst . fr rbellard/pi/. (Cited on p. 128, 227, 229, 234) 20. Lennart Berggren, Jonathan Borwein, Peter Borwein, Pi: A Source Book, Springer-Verlag, New York, 1997. (Cited on p. ll5, 187, 188, 226) 21. Bruce C. Berndt, Ramanujan-l00 Years Old (Fashioned) or 100 Years New (Fangled)'?, The Mathematical Intelligencer, Vol. 10 (1988), No. 3, 24-29. (Cited on p. 105) 22. Bruce C. 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Borwein, Brouwer-Heyting Sequences Converge, Mathematical Intelligencer, Vol. 20, No. 1, 1998, 14-15. (Cited on p. 30) 30. Jonathan M. Borwein and Peter B. Borwein, The Arithmetic-Geometric Mean and Fast Computations 0/ Elementary Functions, SIAM Review, Vol. 26, No. 3 (July 1984), 351-366, aiso in [20, pp. 537-552]. (Cited on p. 114, 236) 31. Jonathan M. Borwein, Peter B. Borwein, More Ramanujan-type Series for 1/7r, Proceedings of the Centenary Conference, Univ. of Illinois at Urbana­ Champaign, June 1-5, 1987, 359-374. 32. Jonathan M. Borwein, Peter B. Borwein, Pi and the AGM - A Study in Analytic Number Theory and Computational Complexity, Wiley, N.Y., 1987. (Cited on p. 7, 59, 73, 74, 90, 92, 114, 188, 228, 229, 237) 33. Jonathan M. Borwein, Pet er B. Borwein, Ramanujan and Pi, Science and Ap­ plications; Supercomputing 88: Volume II, 117-128, 1988. also in [20, p. 588- 595] (Cited on p. 105, 107, 111, 237) 34. Jonathan M. Borwein, Peter B. Borwein, Strange Series and High Precision Praud, American Mathematical Monthly, Vol. 99 (1992), 622-640. (Cited on p. 63, 230) 35. Jonathan M. Borwein, Pet er B. Borwein and K. Dilcher, Pi, Euler Numbers, and Asymptotic Expansions, American Mathematical Monthly, Vol. 96 (1989), 681-687, also in [20, pp. 642-648]. (Cited on p. 156, 157) 36. Jonathan M. Borwein and Roland Girgensohn, Addition theorems and binary expansions, Canadian Journal of Mathematics, Vol. 47 (1995), 262-273. (Cited on p. 48, 235) 37. Richard P. Brent, Fast Multiple-Precision Evaluation 0/ Elementary Func­ tions, Journal of the ACM, Vol. 23, No. 2, April 1976, 242-251, also in [20, pp. 424-433]. (Cited on p. 87) 38. E. Oran Brigham, The Fast Fourier Trans/orm, Prentice Hall, 1994. (Cited on p. 199) 39. David M. Burton, Burton's History 0/ Mathematics: An Introduction, Wm. C. Brown Publishers, Third Edition, 1995. (Cited on p. 14, 190) 40. George S. Carr, Formulas and Theorems in Pure Mathematics, Second Edi­ tion, Chelsea Publishing Company, 1970. (Cited on p. 106) 41. Dario Castellanos, The Ubiquitous 7r, Mathematical Magazine 61 (1988), 67- 98 (Part I) and 148-163 (Part II). (Cited on p. 45, 59, 60, 72, 154, 166, 180, 190, 198, 224, 225, 226, 227, 228, 229,232) 42. Henri Cohen, F. Rodriguez Villegas and Don Zagier Convergence accelera­ tion 0/ alternating series, Experimental Math., to appear. downloadable from http://www.math.u-bordeaux.fr/cohen/ (Cited on p. 150) 43. J.W. Cooley, and J.W.Tukey, An algorithm for the machine calculation 0/ complex Fourier series, Mathematics of Computation Vol. 19 (1965), No. 90, 297-301. (Cited on p. 137) 260 Bibliography 44. James W. Cooley, Peter A.W. Lewis and Peter D. Welch, Historical Notes on the Fast Fourier Trans/orm, Proceedings of the IEEE, Vol. 55 (October 1967), No. 10, 1675-1677. (Cited on p. 199) 45. David A. Cox, The arithmetic-geometric mean 0/ Gauss, L'Enseignment MatMmatique, t. 30 (1984), 275-330, also in [20, pp. 481-536]. (Cited on p. 95, 96, 97, 98) 46. David A. Cox, Gauss and the Arithmetic-Geometric Mean, Notices of the American Mathematical Society 32 (1985), 147-151. (Cited on p. 95) 47. Richard E. Crandall, Projects in Scientific Computation, Springer-Verlag, New York, Inc., 1994. (Cited on p. 230) 48. Jean-Paul Delahaye, Pi - die Story, Birkhäuser-Verlag, Basel, 1999. Französis• che Originalausgabe: Le /ascinant nombre ?T, Pour La Science, 1997. (Cited on p. 50) 49. Drinfel'd, Quadratur des Kreises und Transzendenz von ?T, VEB Deutscher Verlag der Wissenschaften, Berlin, 1980. (Cited on p. 197) 50. Underwood Dudley, Mathematical Cranks, The Mathematical Association of America, 1992. (Cited on p. 8) 51. Heinz-Dieter Ebbinghaus, Reinhold Remmert, et al., Numbers, Springer­ Verlag, New York, 1990. (Cited on p. 56, 168, 170, 176, 213) 52. LeQnhard Euler, Introduction to Analysis 0/ the Infinite, Translation of: In­ troductio in analysin infinitorum, Book I, Translated by John D. Blanton, Springer-Verlag, New York, 1988, Chapter 10 also in [20, pp. 112-128]. (Cited on p. 65, 166, 194) 53. Leonhard Euler, Einleitung in die Analysis des Unendlichen, Erster Teil. Ins Deutsche übertragen von H. Maser, Berlin. Verlag von Julius Springer. 1885. (Cited on p. 166, 194) 54. Martin Gardner, Some comments by Dr. Matrix on symmetrics and reversals, Scientific American, January 1965, 110-116. (Cited on p. 24) 55. Carl Friedrich Gauß, Mathematisches Tagebuch, 1796-1814, Reihe OstwaIds Klassiker der exakten Wissenschaften, Akademische Verlagsgesellschaft Geest & Portig K.-G., Leipzig 1985. Also in [56, X, pp. 483-574]. (Cited on p. 98) 56. Carl Friedrich Gauß, Werke, Göttingen, 1866-1933. (Cited on p. 73, 88, 95, 99, 232) 57. C.F. Gauß, Nachlass zur Theorie des Arithmetisch-Geometrischen Mittels und der Modul/unktion, herausgegeben von Harald Geppert, Reihe Ostwald's Klas­ siker der exakten Wissenschaften, Nr. 225, Akademische Verlagsgesellschaft, Leipzig, 1927. (Cited on p.
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