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A New Proof of Champernowne’s Number is Transcendental

Year 2010, Volume: 2 Issue: 2, 55 - 62, 01.06.2010

S. Narli A.Z. Ozcelik

Abstract

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

Keywords

Algebraic numbers transcendental numbers digits

References

  • 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

Year 2010, Volume: 2 Issue: 2, 55 - 62, 01.06.2010

S. Narli A.Z. Ozcelik

Abstract

References

  • 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
There are 13 citations in total.

Details

Other ID JA65HN63FD
Journal Section Articles
Authors

S. Narli This is me

A.Z. Ozcelik This is me

Publication Date June 1, 2010
Published in Issue Year 2010 Volume: 2 Issue: 2

Cite

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. June 2010;2(2):55-62.
Chicago Narli, S., and A.Z. Ozcelik. “A New Proof of Champernowne’s Number Is Transcendental”. International Journal of Engineering and Applied Sciences 2, no. 2 (June 2010): 55-62.
EndNote Narli S, Ozcelik A (June 1, 2010) A New Proof of Champernowne’s Number is Transcendental. International Journal of Engineering and Applied Sciences 2 2 55–62.
IEEE S. Narli and A. Ozcelik, “A New Proof of Champernowne’s Number is Transcendental”, IJEAS, vol. 2, no. 2, pp. 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 (June 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. and A.Z. Ozcelik. “A New Proof of Champernowne’s Number Is Transcendental”. International Journal of Engineering and Applied Sciences, vol. 2, no. 2, 2010, pp. 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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