Fractions: Continued, Egyptian and Farey
Continued fractions are one of the most delightful and useful subjects of arithmetic, yet they have been continually neglected by our educational factions. Here we discuss their applications as approximating fractions for rational or irrational numbers and functions, their relations with measure theory (and deterministic chaos!), their use in electrical networks and in solving the “squared square;” and the Fibonacci and Lucas numbers and some of their endless applications.
KeywordsEurope Fermat Summing Drone Vinced
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- 5.1C. D. Olds: Continued Fractions (Random House, New York 1963 )Google Scholar
- 5.3A. N. Khovanskii: The Application of Continued Fractions and Their Generalizations to Problems in Approximation Theory ( Noordhoff, Groningen 1963 )Google Scholar
- 5.5C. J. Bouwkamp, A. J. Duijvestijn, P. Medema: Tables relating to simple squared rectangles (Dept. of Mathematics and Mechanics, Technische Hogeschool, Eindhoven 1960 )Google Scholar
- 5.8M. Eigen: “Goethe und das Gestaltproblem in der modernen Biologie,” in H. Rössner (ed.): Rückblick in die Zukunft ( Severin und Siedler, Berlin 1981 )Google Scholar
- 5.10A. Koenig (personal communication)Google Scholar
- 5.11W. Gellert, H. Kästner, M. Hellwich, H. Kästner (eds.): The VNR Concise Encyclopedia of Mathematics ( Van Nostrand Reinhold, New York 1977 )Google Scholar
- 5.12L. K. Hua, Y. Wang: Applications of Number Theory to Numerical Analysis IX. (Springer, Berlin, Heidelberg, New York 1981 )Google Scholar
- 5.13J. C. Lagarias; A. M. Odlyzko: Solving “low-density” subset sum problems. (to be published)Google Scholar
- 5.14R. L. Graham (personal communication)Google Scholar
- 5.15R. K. Guy: Unsolved Problems in Intuitive Mathematics, Vol. I, Number Theory (Springer, Berlin, Heidelberg, New York 1981 )Google Scholar
- 5.16M. Gardner: Mathematical games. Sci. Am. 239,No. 4, 22–26 (1978)Google Scholar
- 5.20C. M. Rader: Recovery of undersampled periodic waveforms. IEEE Trans. ASSP-25, 242–249 (1977)Google Scholar