A New Proof of Champernowne’s Number is Transcendental

S. Narli; A.Z. Ozcelik

A New Proof of Champernowne’s Number is Transcendental

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

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.