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A New Proof of Champernowne’s Number is Transcendental

Yıl 2010, Cilt: 2 Sayı: 2, 55 - 62, 01.06.2010

S. Narli A.Z. Ozcelik

Öz

In this study, a series representation of the number 0,1234...9101112... , which is proved by Kurt MAHLER that it is transcendental, is given and a program which gives the number on an arbitrary digit of 0,1234...9101112... is written. Moreover we proved in a different way that this number is a transcendental one

Anahtar Kelimeler

Algebraic numbers transcendental numbers digits

Kaynakça

  • Hardy, G.H. and Wright, E.M. An Introduction To The Theory of Numbers, Oxford University Press, Ely House,London W.1 ISBN: 0 19853310 1, 1975
  • Niven, I., Zuckerman, H.S. and Montgomery, H.L, An Introduction To The Theory of Numbers, QA241.N56, 512’.7-dc20 Printed in the United States of America, 1991
  • De Spinadel, V.W., On Characterization of the Onset to Chaos. Chaos, Solitons, & Fractals, 8-10, 1997
  • Pickover, C.A, Wonders of Numbers, Oxford University Press, 2000
  • Champernowne, D. G., The Construction of Decimals Normal in the Scale of Ten. J. London Math.Soc.8,1933.
  • Bailey, D. H. and Crandall, R. E. Random Generators and Normal Numbers. Exper. Math. 11, 527-546, 2002.
  • Mahler, K., Lectures on Diophantine Approximations, Part I: g-adic Numbers and Roth's Theorem. Notre Dame, Indiana: University of Notre Dame Press, 1961.
  • Chatterjee S, Yilmaz M. Use of estimated fractal dimension in model identification for time series. J Stat Comput Simulat, 41:129–41, 1992
  • Falconer K., Fractal geometry: mathematical foundations and applications. New York: Springer; 1988
  • Lai, D., Danca. M.F., Fractal and statistical analysis on digits of irrational numbers. Chaos, Solitons and Fractals 36, 246–252, 2008
  • Prasad, G., Rapinchuk, A.S, Zarıskı-Dense Subgroups And Transcendental Number Theory, Math.Res.Let., 12, 239–249, 2005
  • Waldschmidt, M., Transcendence of periods: the state of the art. Pure Appl.Math. Q. 2, 2: 435–463, 2006
  • Mahler, K., Arithmetische Eigenschaften einer Klasse von Dezimalbrüchen, Proc. Konin. Neder. Akad. Wet. Ser. A. 40 p. 421-428, 1937

Yıl 2010, Cilt: 2 Sayı: 2, 55 - 62, 01.06.2010

S. Narli A.Z. Ozcelik

Öz

Kaynakça

  • Hardy, G.H. and Wright, E.M. An Introduction To The Theory of Numbers, Oxford University Press, Ely House,London W.1 ISBN: 0 19853310 1, 1975
  • Niven, I., Zuckerman, H.S. and Montgomery, H.L, An Introduction To The Theory of Numbers, QA241.N56, 512’.7-dc20 Printed in the United States of America, 1991
  • De Spinadel, V.W., On Characterization of the Onset to Chaos. Chaos, Solitons, & Fractals, 8-10, 1997
  • Pickover, C.A, Wonders of Numbers, Oxford University Press, 2000
  • Champernowne, D. G., The Construction of Decimals Normal in the Scale of Ten. J. London Math.Soc.8,1933.
  • Bailey, D. H. and Crandall, R. E. Random Generators and Normal Numbers. Exper. Math. 11, 527-546, 2002.
  • Mahler, K., Lectures on Diophantine Approximations, Part I: g-adic Numbers and Roth's Theorem. Notre Dame, Indiana: University of Notre Dame Press, 1961.
  • Chatterjee S, Yilmaz M. Use of estimated fractal dimension in model identification for time series. J Stat Comput Simulat, 41:129–41, 1992
  • Falconer K., Fractal geometry: mathematical foundations and applications. New York: Springer; 1988
  • Lai, D., Danca. M.F., Fractal and statistical analysis on digits of irrational numbers. Chaos, Solitons and Fractals 36, 246–252, 2008
  • Prasad, G., Rapinchuk, A.S, Zarıskı-Dense Subgroups And Transcendental Number Theory, Math.Res.Let., 12, 239–249, 2005
  • Waldschmidt, M., Transcendence of periods: the state of the art. Pure Appl.Math. Q. 2, 2: 435–463, 2006
  • Mahler, K., Arithmetische Eigenschaften einer Klasse von Dezimalbrüchen, Proc. Konin. Neder. Akad. Wet. Ser. A. 40 p. 421-428, 1937
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Diğer ID JA65HN63FD
Bölüm Makaleler
Yazarlar

S. Narli Bu kişi benim

A.Z. Ozcelik Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2010
Yayımlandığı Sayı Yıl 2010 Cilt: 2 Sayı: 2

Kaynak Göster

APA Narli, S., & Ozcelik, A. (2010). A New Proof of Champernowne’s Number is Transcendental. International Journal of Engineering and Applied Sciences, 2(2), 55-62.
AMA Narli S, Ozcelik A. A New Proof of Champernowne’s Number is Transcendental. IJEAS. Haziran 2010;2(2):55-62.
Chicago Narli, S., ve A.Z. Ozcelik. “A New Proof of Champernowne’s Number Is Transcendental”. International Journal of Engineering and Applied Sciences 2, sy. 2 (Haziran 2010): 55-62.
EndNote Narli S, Ozcelik A (01 Haziran 2010) A New Proof of Champernowne’s Number is Transcendental. International Journal of Engineering and Applied Sciences 2 2 55–62.
IEEE S. Narli ve A. Ozcelik, “A New Proof of Champernowne’s Number is Transcendental”, IJEAS, c. 2, sy. 2, ss. 55–62, 2010.
ISNAD Narli, S. - Ozcelik, A.Z. “A New Proof of Champernowne’s Number Is Transcendental”. International Journal of Engineering and Applied Sciences 2/2 (Haziran 2010), 55-62.
JAMA Narli S, Ozcelik A. A New Proof of Champernowne’s Number is Transcendental. IJEAS. 2010;2:55–62.
MLA Narli, S. ve A.Z. Ozcelik. “A New Proof of Champernowne’s Number Is Transcendental”. International Journal of Engineering and Applied Sciences, c. 2, sy. 2, 2010, ss. 55-62.
Vancouver Narli S, Ozcelik A. A New Proof of Champernowne’s Number is Transcendental. IJEAS. 2010;2(2):55-62.

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