Generalized Fibonacci Sequences PDF Download
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| Author | : Richard A Dunlap |
| Publisher | : World Scientific |
| Total Pages | : 170 |
| Release | : 1997-12-16 |
| Genre | : Mathematics |
| ISBN | : 9814496944 |
Download The Golden Ratio And Fibonacci Numbers Book in PDF, ePub and Kindle
In this invaluable book, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. In addition, the generation of the Fibonacci series and generalized Fibonacci series and their relationship to the golden ratio are presented. These concepts are applied to algorithms for searching and function minimization. The Fibonacci sequence is viewed as a one-dimensional aperiodic, lattice and these ideas are extended to two- and three-dimensional Penrose tilings and the concept of incommensurate projections. The structural properties of aperiodic crystals and the growth of certain biological organisms are described in terms of Fibonacci sequences.
| Author | : Steven Vajda |
| Publisher | : Courier Corporation |
| Total Pages | : 194 |
| Release | : 2008-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486462765 |
Download Fibonacci and Lucas Numbers, and the Golden Section Book in PDF, ePub and Kindle
This survey of the use of Fibonacci and Lucas numbers and the ancient principle of the Golden Section covers areas relevant to operational research, statistics, and computational mathematics. 1989 edition.
| Author | : Yashwant Kumar Panwar |
| Publisher | : LAP Lambert Academic Publishing |
| Total Pages | : 92 |
| Release | : 2012 |
| Genre | : |
| ISBN | : 9783844399288 |
Download Generalized Fibonacci Sequences Book in PDF, ePub and Kindle
The book entitled "Generalized Fibonacci sequences" has been written to meet the requirements of research scholars of Mathematics. This text provides an introduction to the generalized Fibonacci sequences that are typically encountered (and used) in Mathematics and Engineering research scholars.The amount of literature bears witness to the ubiquity of the Fibonacci numbers. Not only are these numbers popular in expository literature because of their beautiful properties, but also the fact that they occur in nature' adds to their fascination. The Fibonacci sequence and generalized Fibonacci sequence are a source of many nice and interesting identities. These numbers are of great importance in the study of many subjects such as algebra, geometry, combinatorics, approximation theory, graph theory and number theory itself. They occur in a variety of other fields such as finance, art, architecture, music, etc. Fibonacci sequence has been generalized in a number of ways. This book is centered on generalization of Fibonacci sequences.
| Author | : R. A. Dunlap |
| Publisher | : World Scientific |
| Total Pages | : 174 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 9789812386304 |
Download The Golden Ratio and Fibonacci Numbers Book in PDF, ePub and Kindle
In this invaluable book, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. In addition, the generation of the Fibonacci series and generalized Fibonacci series and their relationship to the golden ratio are presented. These concepts are applied to algorithms for searching and function minimization. The Fibonacci sequence is viewed as a one-dimensional aperiodic, lattice and these ideas are extended to two- and three-dimensional Penrose tilings and the concept of incommensurate projections. The structural properties of aperiodic crystals and the growth of certain biological organisms are described in terms of Fibonacci sequences. Contents: Basic Properties of the Golden Ratio; Geometric Problems in Two Dimensions; Geometric Problems in Three Dimensions; Fibonacci Numbers; Lucas Numbers and Generalized Fibonacci Numbers; Continued Fractions and Rational Approximants; Generalized Fibonacci Representation Theorems; Optimal Spacing and Search Algorithms; Commensurate and Incommensurate Projections; Penrose Tilings; Quasicrystallography; Biological Applications; Construction of the Regular Pentagon; The First 100 Fibonacci and Lucas Numbers; Relationships Involving the Golden Ratio and Generalized Fibonacci Numbers. Readership: Applied mathematicians.
| Author | : Hee Sik Kim |
| Publisher | : Infinite Study |
| Total Pages | : 10 |
| Release | : |
| Genre | : |
| ISBN | : |
Download Generalized Fibonacci sequences in groupoids Book in PDF, ePub and Kindle
In this paper, we introduce the notion of generalized Fibonacci sequences over a groupoid and discuss it in particular for the case where the groupoid contains idempotents and pre-idempotents.
| Author | : Paul Stanley Fisher |
| Publisher | : |
| Total Pages | : 66 |
| Release | : 1965 |
| Genre | : Matrices |
| ISBN | : |
Download Generalized Fibonacci Sequences Book in PDF, ePub and Kindle
| Author | : Thomas Koshy |
| Publisher | : OUP USA |
| Total Pages | : 439 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 019533454X |
Download Catalan Numbers with Applications Book in PDF, ePub and Kindle
This book presents a clear and comprehensive introduction to one of the truly fascinating topics in mathematics: Catalan numbers. They crop up in chess, computer programming and even train tracks. In addition to lucid descriptions of the mathematics and history behind Catalan numbers, Koshy includes short biographies of the prominent mathematicians who have worked with the numbers.
| Author | : Arthur T. Benjamin |
| Publisher | : American Mathematical Society |
| Total Pages | : 210 |
| Release | : 2022-09-21 |
| Genre | : Mathematics |
| ISBN | : 1470472597 |
Download Proofs that Really Count Book in PDF, ePub and Kindle
Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.
| Author | : Hee Sik Kim |
| Publisher | : Infinite Study |
| Total Pages | : 10 |
| Release | : |
| Genre | : |
| ISBN | : |
Download Generalized Fibonacci sequences in groupoids Book in PDF, ePub and Kindle
In this paper, we introduce the notion of generalized Fibonacci sequences over a groupoid and discuss it in particular for the case where the groupoid contains idempotents and pre-idempotents. Using the notion of Smarandache-type P-algebra, we obtain several relations on groupoids which are derived from generalized Fibonacci sequences.
| Author | : Laurence Sigler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 736 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461300797 |
Download Fibonacci’s Liber Abaci Book in PDF, ePub and Kindle
First published in 1202, Fibonacci’s Liber Abaci was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe. This is the first translation into a modern European language, of interest not only to historians of science but also to all mathematicians and mathematics teachers interested in the origins of their methods.
