Golden Sequences and Infinite Series PDF Download
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Author: N. P. Bali
Publisher: Firewall Media
ISBN: 9788131800553
Category :
Languages : en
Pages : 342
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Book Description
Author: N. P. Bali
Publisher: Firewall Media
ISBN: 9788131800553
Category :
Languages : en
Pages : 342
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Book Description
Author: N.P. Bali
Publisher: Firewall Media
ISBN: 9788170080145
Category : Mathematical analysis
Languages : en
Pages : 822
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Book Description
Author: Pedro Hugo Garcia Pelaez
Publisher:
ISBN: 9781370335138
Category :
Languages : en
Pages :
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Book Description
Author: R. A. Dunlap
Publisher: World Scientific
ISBN: 9789812386304
Category : Mathematics
Languages : en
Pages : 174
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Book Description
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: Bach, Jr. (Bernhard W.)
Publisher:
ISBN: 9781107446588
Category :
Languages : en
Pages : 202
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Book Description
Author: Konrad Knopp
Publisher:
ISBN:
Category : Secuencias (matematicas)
Languages : en
Pages : 186
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Book Description
Author: Bernhard W. Bach, Jr.
Publisher: Cambridge University Press
ISBN: 1108645739
Category : Science
Languages : en
Pages : 201
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Book Description
Why study infinite series? Not all mathematical problems can be solved exactly or have a solution that can be expressed in terms of a known function. In such cases, it is common practice to use an infinite series expansion to approximate or represent a solution. This informal introduction for undergraduate students explores the numerous uses of infinite series and sequences in engineering and the physical sciences. The material has been carefully selected to help the reader develop the techniques needed to confidently utilize infinite series. The book begins with infinite series and sequences before moving onto power series, complex infinite series and finally onto Fourier, Legendre, and Fourier-Bessel series. With a focus on practical applications, the book demonstrates that infinite series are more than an academic exercise and helps students to conceptualize the theory with real world examples and to build their skill set in this area.
Author: David G. Green
Publisher: IOS Press
ISBN: 9789051991178
Category : Biological systems
Languages : en
Pages : 402
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Book Description
Author: Manfred Schroeder
Publisher: Courier Corporation
ISBN: 0486472043
Category : Science
Languages : en
Pages : 450
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Book Description
This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author -- hailed by Publishers Weekly as a modern Lewis Carroll -- conveys memorable insights in the form of puns and puzzles. 1992 edition.
Author: Alfred S. Posamentier
Publisher: Prometheus Books
ISBN: 1615920226
Category : Mathematics
Languages : en
Pages : 385
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Book Description
The most ubiquitous, and perhaps the most intriguing, number pattern in mathematics is the Fibonacci sequence. In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few. Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.
