Recent knowledge of the number π

Ivan Netuka; Jiří Veselý

Pokroky matematiky, fyziky a astronomie (1998)

  • Volume: 43, Issue: 3, page 217-236
  • ISSN: 0032-2423

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Netuka, Ivan, and Veselý, Jiří. "Nedávné poznatky o čísle $\pi $." Pokroky matematiky, fyziky a astronomie 43.3 (1998): 217-236. <http://eudml.org/doc/35257>.

@article{Netuka1998,
author = {Netuka, Ivan, Veselý, Jiří},
journal = {Pokroky matematiky, fyziky a astronomie},
keywords = {; normality; computational methods; numerical algorithms},
language = {cze},
number = {3},
pages = {217-236},
publisher = {Jednota českých matematiků a fyziků Union of Czech Mathematicians and Physicists},
title = {Nedávné poznatky o čísle $\pi $},
url = {http://eudml.org/doc/35257},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Netuka, Ivan
AU - Veselý, Jiří
TI - Nedávné poznatky o čísle $\pi $
JO - Pokroky matematiky, fyziky a astronomie
PY - 1998
PB - Jednota českých matematiků a fyziků Union of Czech Mathematicians and Physicists
VL - 43
IS - 3
SP - 217
EP - 236
LA - cze
KW - ; normality; computational methods; numerical algorithms
UR - http://eudml.org/doc/35257
ER -

References

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  1. Adamchik, V., Wagon, S., π : A 2000-year-old search changes direction, Mathematica in Education and Research 5 (1996), 11–19 (text článku lze nalézt v elektronické podobě na URL adrese <http://www.wolfram.com/~victor/articles/pi/pi.html>). (1996) 
  2. Adamchik, V., Wagon, S., A simple formula for π , Amer. Math. Monthly 104 (1997), 852–855. (1997) Zbl0886.11073MR1479991
  3. Bailey, D. H., A polynomial time, numerically stable integer relation algorithm, NAS Technical Report Server (RNR-91-032, December 1991). (1991) 
  4. Bailey, D. H., Borwein, P. B., Plouffe, S., On the rapid computation of various polylogarithmic constants, Math. Comp. 66 (1997), 903–913. (1997) Zbl0879.11073MR1415794
  5. Bailey, D. H., Ferguson, H. R. P., Numerical results on relations between fundamental constants using a new algorithm, Math. Comp. 53 (1989), 649–656 (*). (1989) Zbl0687.10002MR0979934
  6. Bailey, D. H., Plouffe, S., Recognizing numerical constants, Organic mathematics (Burnaby, BC, 1995), CMS Conf. Proc. 20 (1977), Amer. Math. Soc., Providence, RI, 73–88 (preprint z r. 1995). (1977) Zbl0898.11049MR1483914
  7. Bailey, D. H., Borwein, J. M., Borwein, P. B., Plouffe, S., The quest for Pi, Math. Intelligencer 19 (1997), no. 1, 50–57. (1997) Zbl0878.11002MR1439159
  8. Beckmann, P., Historie čísla π , Academia, Praha 1998 (překlad 5. vydání z r. 1982). (1998) 
  9. Bellard, F., [unknown], <http://www-stud.enst.fr/~bellard/pi-challenge/index.html> a dále <http://www-stud.enst.fr/~bellard/pi-challenge/announce220997.html>. 
  10. Berggren, L., Borwein, J. M., Borwein, P. B., π : A source book, Springer, New York 1997. (1997) Zbl0876.11001MR1467531
  11. Borwein, J. M., Borwein, P. B., The arithmetic-geometric mean and fast computation of elementary functions, SIAM Rev. 26 (1984), 351–366 (*). (1984) Zbl0557.65009MR0750454
  12. Borwein, J. M., Borwein, P. B., Pi and the AGM: A study in analytic number theory and computational complexity, John Wiley & Sons, New York 1987. (1987) Zbl0611.10001MR0877728
  13. Borwein, J. M., Borwein, P. B., Ramanujan and Pi, Science and applications; Supercomputing 88, Vol. II (1988), 112–117 (*). (1988) 
  14. Borwein, J. M., Borwein, P. B., Dilcher, K., π , Euler numbers and asymptotic expansion, Amer. Math. Monthly 96 (1989), 681–687 (*). (1989) Zbl0711.11009MR1019148
  15. Borwein, J. M., Borwein, P. B., Girgensohn, R., Parnes, S., Making sense of experimental mathematics, Math. Intelligencer 18 (1996), no. 4, 12–18 (preprint s názvem “Experimental mathematics: a discussion” z r. 1995 je k dispozici na serveru CECM, viz [23]). (1996) Zbl0874.00027MR1413248
  16. Borwein, J. M., Borwein, P. B., Bailey, D. H., Ramanujan, modular equations, and approximations to Pi or How to compute one bilion digits of Pi, Amer. Math. Monthly 96 (1989), 201–219 (*). (1989) Zbl0672.10017MR0991866
  17. Brent, R. P., Fast multiple-precision evaluation of elementary functions, J. Assoc. Comput. Mach. 23 (1976), 242–251 (*). (1976) Zbl0324.65018MR0395314
  18. Castellanos, D., The ubiquitous π , Math. Magazin 61 (1988), 67–98 a 149–163. (1988) Zbl0654.10002MR0934824
  19. Goldstine, H. H., A history of numerical analysis from the 16th through the 19th century, Springer, New York 1977. (1977) Zbl0402.01005MR0484905
  20. Hančl, J., Two proofs of transcendency of  π and e, Czech. Math. Journal 35 (1985), 543–549. (1985) Zbl0587.10017MR0809040
  21. Iwamoto, Y., A proof that π 2 is irrational, J. Osaka Inst. Sci. Tech. 1 (1949), 147–148. (1949) Zbl0037.31406MR0037863
  22. Jarník, V., Diferenciální počet I, Academia, Praha 1984 (6. vydání). (1984) 
  23. Kanada, Y., [unknown], <ftp://www.cc.u-tokyo.ac.jp/readme.our_latest_record> (lze také nalézt na adrese <http://cecm.sfu.ca/personal/jborwein/Kanada_50b.html>). Zbl1052.68668
  24. Kořínek, V., Základy algebry, NČSAV, Praha 1953. (1953) MR0075914
  25. Knopp, K., Theorie und Anwendungen der unendlichen Reihen, Springer, Berlin 1924. (1924) Zbl50.0150.12MR0028430
  26. Niven, I., A simple proof that π is irrational, Bull. Amer. Math. Soc. 53 (1947), 509 (*). (1947) Zbl0037.31404MR0021013
  27. Novák, B., O sedmém Hilbertově problému, Pokroky MFA 17 (1972), 245–256. (1972) 
  28. Novák, B., A remark to a paper of J. F. Koksma, Nieuw Arch. voor Wiskunde 23 (1975), 195–197. (1975) Zbl0313.10033MR0406941
  29. Novák, B., Vybrané kapitoly z teorie čísel, SPN, Praha 1972. (1972) 
  30. Plouffe, S., [unknown], <http://www.lacim.uqam.ca/ploufe/Simon/results.html>. Zbl1010.11071
  31. Rabinowitz, S. D., Wagon, S., A spigot algorithm for the digits of π , Amer. Math. Monthly 103 (1995), 195–203. (1995) Zbl0853.11102MR1317842
  32. Ramanujan, S., Modular equations and approximations to π , Quart. J. Math. 45 (1914), 350–372. (1914) Zbl45.1249.01
  33. Salamin, E., Computation of π using arithmetic-geometric mean, Math. Comp. 30 (1976), 565–570 (*). (1976) Zbl0345.10003MR0404124
  34. Taylor, S. J., Pravidelnost náhodnosti, Pokroky MFA 25 (1980), 28–34 (překlad). (1980) 
  35. Veselý, J., π aneb 3,14159.., Učitel matematiky 3 (15), 4 (16) (1995), 1–10 a 1–13. (1995) 
  36. Veselý, J., Matematická analýza pro učitele, Matfyzpress, vydavatelství MFF UK, Praha 1997. (1997) 
  37. Wagon, S., Is Pi normal?, Math. Inteligencer 7 (1985), no. 3, 65–67 (*). (1985) Zbl0565.10002MR0795541
  38. Williams, R., [unknown], <http://www.ccsf.caltech.edu/~roy/pi.formulas.html>. Zbl1200.57005
  39. Borwein, J. M., Brouwer-Heyting sequence converge, Math. Intelligencer 20 (1998), no. 1, 14–15. (1998) Zbl0921.00003MR1601815

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