| Title:
|
Nedávné poznatky o čísle $\pi$ (Czech) |
| Title:
|
Recent knowledge of the number $\pi$ (English) |
| Author:
|
Netuka, Ivan |
| Author:
|
Veselý, Jiří |
| Language:
|
Czech |
| Journal:
|
Pokroky matematiky, fyziky a astronomie |
| ISSN:
|
0032-2423 |
| Volume:
|
43 |
| Issue:
|
3 |
| Year:
|
1998 |
| Pages:
|
217-236 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11-01 |
| MSC:
|
11Y16 |
| MSC:
|
11Y60 |
| idZBL:
|
Zbl 0936.11001 |
| . |
| Date available:
|
2010-12-11T16:43:52Z |
| Last updated:
|
2012-08-25 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137587 |
| . |
| Reference:
|
[1] Adamchik, V., Wagon, S.: $\pi $: 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>). |
| Reference:
|
[2] Adamchik, V., Wagon, S.: A simple formula for $\pi $.Amer. Math. Monthly 104 (1997), 852–855. Zbl 0886.11073, MR 1479991 |
| Reference:
|
[3] Bailey, D. H.: A polynomial time, numerically stable integer relation algorithm.NAS Technical Report Server (RNR-91-032, December 1991). |
| Reference:
|
[4] Bailey, D. H., Borwein, P. B., Plouffe, S.: On the rapid computation of various polylogarithmic constants.Math. Comp. 66 (1997), 903–913. Zbl 0879.11073, MR 1415794 |
| Reference:
|
[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 (*). Zbl 0687.10002, MR 0979934 |
| Reference:
|
[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). MR 1483914 |
| Reference:
|
[7] Bailey, D. H., Borwein, J. M., Borwein, P. B., Plouffe, S.: The quest for Pi.Math. Intelligencer 19 (1997), no. 1, 50–57. Zbl 0878.11002, MR 1439159 |
| Reference:
|
[8] Beckmann, P.: Historie čísla $\pi $.Academia, Praha 1998 (překlad 5. vydání z r. 1982). |
| Reference:
|
[9] Bellard, F.: .<http://www-stud.enst.fr/~bellard/pi-challenge/index.html> a dále <http://www-stud.enst.fr/~bellard/pi-challenge/announce220997.html>. |
| Reference:
|
[10] Berggren, L., Borwein, J. M., Borwein, P. B.: $\pi $: A source book.Springer, New York 1997. Zbl 0876.11001, MR 1467531 |
| Reference:
|
[11] Borwein, J. M., Borwein, P. B.: The arithmetic-geometric mean and fast computation of elementary functions.SIAM Rev. 26 (1984), 351–366 (*). Zbl 0557.65009, MR 0750454 |
| Reference:
|
[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. Zbl 0611.10001, MR 0877728 |
| Reference:
|
[13] Borwein, J. M., Borwein, P. B.: Ramanujan and Pi.Science and applications; Supercomputing 88, Vol. II (1988), 112–117 (*). |
| Reference:
|
[14] Borwein, J. M., Borwein, P. B., Dilcher, K.: $\pi $, Euler numbers and asymptotic expansion.Amer. Math. Monthly 96 (1989), 681–687 (*). MR 1019148 |
| Reference:
|
[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]). Zbl 0874.00027, MR 1413248 |
| Reference:
|
[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 (*). MR 0991866 |
| Reference:
|
[17] Brent, R. P.: Fast multiple-precision evaluation of elementary functions.J. Assoc. Comput. Mach. 23 (1976), 242–251 (*). Zbl 0324.65018, MR 0395314 |
| Reference:
|
[18] Castellanos, D.: The ubiquitous $\pi $.Math. Magazin 61 (1988), 67–98 a 149–163. Zbl 0654.10002, MR 0934824 |
| Reference:
|
[19] Goldstine, H. H.: A history of numerical analysis from the 16th through the 19th century.Springer, New York 1977. Zbl 0402.01005, MR 0484905 |
| Reference:
|
[20] Hančl, J.: Two proofs of transcendency of $\pi $ and e.Czech. Math. Journal 35 (1985), 543–549. MR 0809040 |
| Reference:
|
[21] Iwamoto, Y.: A proof that $\pi ^2$ is irrational.J. Osaka Inst. Sci. Tech. 1 (1949), 147–148. MR 0037863 |
| Reference:
|
[22] Jarník, V.: Diferenciální počet I.Academia, Praha 1984 (6. vydání). |
| Reference:
|
[23] Kanada, Y.: .<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>). Zbl 1052.68668 |
| Reference:
|
[24] Kořínek, V.: Základy algebry.NČSAV, Praha 1953. MR 0075914 |
| Reference:
|
[25] Knopp, K.: Theorie und Anwendungen der unendlichen Reihen.Springer, Berlin 1924. MR 0028430 |
| Reference:
|
[26] Niven, I.: A simple proof that $\pi $ is irrational.Bull. Amer. Math. Soc. 53 (1947), 509 (*). Zbl 0037.31404, MR 0021013 |
| Reference:
|
[27] Novák, B.: O sedmém Hilbertově problému.Pokroky MFA 17 (1972), 245–256. |
| Reference:
|
[28] Novák, B.: A remark to a paper of J. F. Koksma.Nieuw Arch. voor Wiskunde 23 (1975), 195–197. MR 0406941 |
| Reference:
|
[29] Novák, B.: Vybrané kapitoly z teorie čísel.SPN, Praha 1972. |
| Reference:
|
[30] Plouffe, S.: .<http://www.lacim.uqam.ca/ploufe/Simon/results.html>. Zbl 1010.11071 |
| Reference:
|
[31] Rabinowitz, S. D., Wagon, S.: A spigot algorithm for the digits of $\pi $.Amer. Math. Monthly 103 (1995), 195–203. Zbl 0853.11102, MR 1317842 |
| Reference:
|
[32] Ramanujan, S.: Modular equations and approximations to $\pi $.Quart. J. Math. 45 (1914), 350–372. |
| Reference:
|
[33] Salamin, E.: Computation of $\pi $ using arithmetic-geometric mean.Math. Comp. 30 (1976), 565–570 (*). Zbl 0345.10003, MR 0404124 |
| Reference:
|
[34] Taylor, S. J.: Pravidelnost náhodnosti.Pokroky MFA 25 (1980), 28–34 (překlad). |
| Reference:
|
[35] Veselý, J.: $\pi $ aneb 3,14159...Učitel matematiky 3 (15), 4 (16) (1995), 1–10 a 1–13. |
| Reference:
|
[36] Veselý, J.: Matematická analýza pro učitele.Matfyzpress, vydavatelství MFF UK, Praha 1997. |
| Reference:
|
[37] Wagon, S.: Is Pi normal?.Math. Inteligencer 7 (1985), no. 3, 65–67 (*). Zbl 0565.10002, MR 0795541 |
| Reference:
|
[38] Williams, R.: .<http://www.ccsf.caltech.edu/~roy/pi.formulas.html>. Zbl 1200.57005 |
| Reference:
|
[39] Borwein, J. M.: Brouwer-Heyting sequence converge.Math. Intelligencer 20 (1998), no. 1, 14–15. MR 1601815 |
| . |
