## Fibonacci and Lucas Numbers, and the Golden Section: Theory and ApplicationsThis text for advanced undergraduates and graduate students surveys the use of Fibonacci and Lucas numbers in areas relevant to operational research, statistics, and computational mathematics. It also covers geometric topics related to the ancient principle known as the Golden Section--a mystical expression of aesthetic harmony that bears a close connection with the Fibonacci mechanism. The Fibonacci principle of forming a new number by an appropriate combination of previous numbers has been extended to yield sequences with surprising and sometimes mystifying properties: the Meta-Fibonacci sequences. This text examines Meta-Fibonacci numbers, proceeding to a survey of the Golden Section in the plane and space. It also describes Platonic solids and some of their less familiar features, and an appendix and other supplements offer helpful background information. Students and teachers will find this book relevant to studies of algebra, geometry, probability theory, computational aspects, and combinatorial aspects of number theory. Steven Vajda was born in Budapest in 1901 and died in England in 1995. For the last twenty-two years of his life, he was Visiting Professor of Mathematics at Sussex University. As a prominent teacher, lecturer, and author he played a vital role in the development of mathematical programming and operations research and wrote more than a dozen books and many research papers on these and other topics including game theory. |

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a-number appear Assume b-number binomial coefﬁcients brieﬂy canonical representation Carlitz centre Chapter circumcircle circumradius common factor compute congruent Conolly Consider contain continued fraction convergents coordinates cosh nz cycle deﬁned deﬁnition denote diagonal difference equation divisible by F dodecahedron E 0(mod edge length equals Euclidean algorithm example Fibonacci numbers Fibonacci sequence ﬁgure ﬁnd ﬁrst ﬁxed Fn+1 follows form 5t formula Golden Rectangle Golden Section Golden Section Search hence highest power holds hyperbolic functions icosahedron inﬁnite inradius instance interval larger lemma linear Lucas numbers Lucas sequence mentioned multiple obtain octahedron octave odd prime pairs period pile positive integer possible prime number primes which divide problem quadratic residue modulo ratio recurrence regular pentagon relatively prime replace right-hand side root run-up safe point seed sequence modulo smallest residues solution square starting subscript Theorem tosses triangle Tribonacci uniform values vertices write