Fibonacci Numbers and Their Applications (Google eBook)

Front Cover
Andreas N. Philippou, Gerald E. Bergum, A. F. Horadam
Springer Science & Business Media, Jan 1, 1986 - Mathematics - 304 pages
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Contents

VIII
1
IX
9
X
39
XI
43
XII
55
XIII
81
XIV
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XV
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181
XXI
185
XXII
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XXIII
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XXIV
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XXV
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XXVI
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XXVII
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XVI
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XVIII
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XIX
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XXVIII
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XXIX
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Page viii - As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company they drew from each other fresh vitality and thenceforward marched on at a rapid pace towards perfection.
Page vii - completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics. This programme. Mathematics and Its Applications, is devoted to new emerging (sub)disciplines and to such (new) interrelations as exempla gratia: - a central concept which plays an important role in several different mathematical and/or scientific specialized areas; - new applications of the...
Page vii - Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years:...
Page vii - Chesterton. The Scandal of Father "The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin', van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches.
Page vii - It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum...
Page vi - Erik Lieuwens 131 FIBONACCI AND LUCAS NUMBERS AND THE MORGAN-VOYCE POLYNOMIALS IN LADDER NETWORKS AND IN ELECTRIC LINE THEORY Joseph Lahr 141 INFINITE SERIES SUMMATION INVOLVING RECIPROCALS OF PELL POLYNOMIALS Br.
Page ii - Universita degli Studi di Roma, Italy Yu. I. MANIN, Steklov Institute of Mathematics, Moscow, USSR AHG RINNOOY KAN, Erasmus University, Rotterdam, The Netherlands G.-C. ROTA, MIT, Cambridge, Mass., USA Shang-Ching Chou Institute for Computing Science, University of Texas at Austin, Texas, USA Mechanical Geometry Theorem Proving D.
Page viii - ... along separate paths, their advance was slow and their applications limited. Eugene Wigner But when these sciences joined company they drew from each other fresh vitality and Well, if you know of a better 'ole, go to it. thenceforward marched on at a rapid pace towards perfection. Bruce Bairnsfather Joseph Louis Lagrange. What is now proved was once only imagined.

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