From The Golden Rectangle To The Fibonacci Sequences

Author : Opher Liba,Bat-Sheva Ilany
Publisher : Springer Nature
Page : 174 pages
File Size : 51,9 Mb
Release : 2023-05-08
Category : Education
ISBN : 9783030976002

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From the Golden Rectangle to the Fibonacci Sequences by Opher Liba,Bat-Sheva Ilany Pdf

The book takes us on a fascinating journey through one of the most beautiful and fascinating topics of mathematics. It presents a wealth of information about the golden ratio and the Fibonacci sequence. The book introduces the reader to novel perspectives to classic mathematical concepts and problems. The book’s structure engages with the reader actively, leading to more profound understanding, satisfaction and deep insights in learning mathematics. The book strengthens and expands the readers' mathematical knowledge, allowing them a glimpse of several advanced academic concepts. It demonstrates and instils the essence of mathematical research, along the lines of George Polya: observation, conjecture, proof, implementation, generalization and raising new questions.

Author : Richard A Dunlap
Publisher : World Scientific
Page : 172 pages
File Size : 42,9 Mb
Release : 1997-12-16
Category : Mathematics
ISBN : 9789814496940

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The Golden Ratio And Fibonacci Numbers by Richard A Dunlap Pdf

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
Page : 194 pages
File Size : 42,9 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780486462769

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Fibonacci and Lucas Numbers, and the Golden Section by Steven Vajda Pdf

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 : Krassimir T. Atanassov
Publisher : World Scientific
Page : 334 pages
File Size : 52,6 Mb
Release : 2002
Category : Mathematics
ISBN : 9812381341

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New Visual Perspectives on Fibonacci Numbers by Krassimir T. Atanassov Pdf

Discusses new ground on Fibonacci sequences and the well-known Fibonacci numbers. There is a continuing emphasis on diagrams, both geometric and combinatorial, which helps to tie disparate topics together, weaving around the unifying themes of the golden mean and various generalizations of the Fibonacci recurrence relation.

Author : Doug Patt
Publisher : MIT Press
Page : 138 pages
File Size : 53,7 Mb
Release : 2012-02-17
Category : Architecture
ISBN : 9780262516990

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How to Architect by Doug Patt Pdf

The basics of the profession and practice of architecture, presented in illustrated A-Z form. The word "architect" is a noun, but Doug Patt uses it as a verb—coining a term and making a point about using parts of speech and parts of buildings in new ways. Changing the function of a word, or a room, can produce surprise and meaning. In How to Architect, Patt—an architect and the creator of a series of wildly popular online videos about architecture—presents the basics of architecture in A-Z form, starting with "A is for Asymmetry" (as seen in Chartres Cathedral and Frank Gehry), detouring through "N is for Narrative," and ending with "Z is for Zeal" (a quality that successful architects tend to have, even in fiction—see The Fountainhead's architect-hero Howard Roark.) How to Architect is a book to guide you on the road to architecture. If you are just starting on that journey or thinking about becoming an architect, it is a place to begin. If you are already an architect and want to remind yourself of what drew you to the profession, it is a book of affirmation. And if you are just curious about what goes into the design and construction of buildings, this book tells you how architects think. Patt introduces each entry with a hand-drawn letter, and accompanies the text with illustrations that illuminate the concept discussed: a fallen Humpty Dumpty illustrates the perils of fragile egos; photographs of an X-Acto knife and other hand tools remind us of architecture's nondigital origins. How to Architect offers encouragement to aspiring architects but also mounts a defense of architecture as a profession—by calling out a defiant verb: architect!

Author : Hans Walser
Publisher : American Mathematical Soc.
Page : 142 pages
File Size : 46,7 Mb
Release : 2020-08-03
Category : Mathematics
ISBN : 9781470457495

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The Golden Section by Hans Walser Pdf

Author : Alfred S. Posamentier,Ingmar Lehmann
Publisher : Unknown
Page : 406 pages
File Size : 54,8 Mb
Release : 2007
Category : Mathematics
ISBN : STANFORD:36105123270576

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The Fabulous Fibonacci Numbers by Alfred S. Posamentier,Ingmar Lehmann Pdf

Explores the complexity and wide-ranging applications of the Fibonacci sequence, which appears in nature, art, economics, and the "golden ratio," which is derived from this simple pattern of numbers.

Author : Roger Herz-Fischler
Publisher : Courier Corporation
Page : 228 pages
File Size : 48,9 Mb
Release : 2013-12-31
Category : Mathematics
ISBN : 9780486152325

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A Mathematical History of the Golden Number by Roger Herz-Fischler Pdf

This comprehensive study traces the historic development of division in extreme and mean ratio ("the golden number") from its first appearance in Euclid's Elements through the 18th century. Features numerous illustrations.

Author : K. K. Tung
Publisher : Princeton University Press
Page : 319 pages
File Size : 52,5 Mb
Release : 2016-06-14
Category : Mathematics
ISBN : 9781400884056

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Topics in Mathematical Modeling by K. K. Tung Pdf

Topics in Mathematical Modeling is an introductory textbook on mathematical modeling. The book teaches how simple mathematics can help formulate and solve real problems of current research interest in a wide range of fields, including biology, ecology, computer science, geophysics, engineering, and the social sciences. Yet the prerequisites are minimal: calculus and elementary differential equations. Among the many topics addressed are HIV; plant phyllotaxis; global warming; the World Wide Web; plant and animal vascular networks; social networks; chaos and fractals; marriage and divorce; and El Niño. Traditional modeling topics such as predator-prey interaction, harvesting, and wars of attrition are also included. Most chapters begin with the history of a problem, follow with a demonstration of how it can be modeled using various mathematical tools, and close with a discussion of its remaining unsolved aspects. Designed for a one-semester course, the book progresses from problems that can be solved with relatively simple mathematics to ones that require more sophisticated methods. The math techniques are taught as needed to solve the problem being addressed, and each chapter is designed to be largely independent to give teachers flexibility. The book, which can be used as an overview and introduction to applied mathematics, is particularly suitable for sophomore, junior, and senior students in math, science, and engineering.

Author : R. A. Dunlap
Publisher : Unknown
Page : 128 pages
File Size : 47,5 Mb
Release : 1997
Category : Fibonacci numbers
ISBN : OCLC:1035782028

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The Golden Ratio and Fibonacci Numbers by R. A. Dunlap Pdf

Author : K T Atanassov,V Atanassova,A G Shannon,J C Turner
Publisher : World Scientific
Page : 332 pages
File Size : 44,9 Mb
Release : 2002-10-01
Category : Mathematics
ISBN : 9789814487795

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New Visual Perspectives on Fibonacci Numbers by K T Atanassov,V Atanassova,A G Shannon,J C Turner Pdf

This book covers new ground on Fibonacci sequences and the well-known Fibonacci numbers. It will appeal to research mathematicians wishing to advance the new ideas themselves, and to recreational mathematicians, who will enjoy the various visual approaches and the problems inherent in them. There is a continuing emphasis on diagrams, both geometric and combinatorial, which helps to tie disparate topics together, weaving around the unifying themes of the golden mean and various generalizations of the Fibonacci recurrence relation. Very little prior mathematical knowledge is assumed, other than the rudiments of algebra and geometry, so the book may be used as a source of enrichment material and project work for college students. A chapter on games using goldpoint tiles is included at the end, and it can provide much material for stimulating mathematical activities involving geometric puzzles of a combinatoric nature. Contents:Number Theoretic Perspectives — Coupled Recurrence Relations:Introductory Remarks by the First AuthorThe 2–Fibonacci SequencesExtensions of the Concepts of 2–Fibonacci SequencesOther Ideas for Modification of the Fibonacci SequencesNumber Theoretic Perspectives—Number Trees:Introduction — Turner's Number TreesGeneralizations Using TableauxOn Gray Codes and Coupled Recurrence TreesStudies of Node Sums on Number TreesConnections with Pascal–T TrianglesGeometric Perspectives — Finonacci Vector Geometry:Introduction and Elementary ResultsVector Sequences from Linear RecurrencesThe Fibonacci Honeycomb PlaneFibonacci and Lucas Vector PolygonsTrigonometry in the Honeycomb PlaneVector Sequences Generated in PlanesFibonacci Tracks, Groups, and Plus–Minus SequencesGeometric Perspectives — Goldpoint Geometry:On Goldpoints and Golden-Mean ConstructionsThe Goldpoint Rings of a Line-SegmentSome Fractals in Goldpoint GeometryTriangles and Squares Marked with GoldpointsPlane Tessellations with Goldpoint TrianglesTessellations with Goldpoint SquaresGames with Goldpoint Tiles Readership: Researchers, academics, college teachers and general readers interested in Fibonacci mathematics. Keywords:Reviews:“… the authors explored many applications of the Fibonacci-type sequences that are new and point the way to many additional lines of study. Their ideas were original and well-described and I recommend this book to anyone interested in iterative processes on integers.”MAA Online Book Review “Altogether this is a very stimulating book.”Mathematics Abstracts “… much of the number-theoretical work gains a good deal of interest if the reader has some knowledge of these traditional results and techniques.”New Zealand Mathematical Society Newsletter “Vorobiev's book presents a solid overview, perfectly pitched to undergraduates … it speaks to a more sophisticated audience and reflects the new developments of the intervening years, especially the beautiful role of Fibonacci numbers in Matiyasevich's groundbreaking negative solution of Hilbert's tenth problem.”Choice

Author : Laurence Sigler
Publisher : Springer Science & Business Media
Page : 736 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461300793

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Fibonacci’s Liber Abaci by Laurence Sigler Pdf

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.

Author : S. Vajda
Publisher : Unknown
Page : 202 pages
File Size : 42,8 Mb
Release : 1989
Category : Fibonacci numbers
ISBN : CORNELL:31924051551723

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Fibonacci & Lucas Numbers, and the Golden Section by S. Vajda Pdf

Author : IntroBooks
Publisher : Can Akdeniz
Page : 40 pages
File Size : 52,6 Mb
Release : 2019-01-16
Category : Electronic
ISBN : 8210379456XXX

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The Fibonacci Sequence by IntroBooks Pdf

The Fibonacci sequence is a great way by which the different patterns can be noticed and understood. The Fibonacci sequence is used by a number of mathematicians, philosophers, architects, etc. The Fibonacci sequence was also used for the creation of some great buildings. The Fibonacci sequence is an amazing technique and probably the only one technique, which is present in a number of domains such as mathematics, art, architecture, etc. The Golden Ratio is directly related to nature, which makes it even more interesting and easy going. It has not only appeared in the man-made things but it is also involved in a number of natural things. This came as a surprise to everyone, who is involved in the development of the mankind, educational and academic regions. The Fibonacci sequence is an ancient technique which is still famous and used in a variety of forms. The spiral of the Fibonacci, the sequence and the numbers play a great role in the studies of different arenas.

Author : Mario Livio
Publisher : Crown
Page : 305 pages
File Size : 40,8 Mb
Release : 2008-11-12
Category : Mathematics
ISBN : 9780307485526

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The Golden Ratio by Mario Livio Pdf

Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market! The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.