The Golden Ratio And Fibonacci Numbers

The Golden Ratio And Fibonacci Numbers
Author: Richard A Dunlap
Publisher: World Scientific
Total Pages: 170
Release: 1997-12-16
Genre: Mathematics
ISBN: 9814496944

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.

Fibonacci’s Liber Abaci

Fibonacci’s Liber Abaci
Author: Laurence Sigler
Publisher: Springer Science & Business Media
Total Pages: 736
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461300797

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.

How to Architect

How to Architect
Author: Doug Patt
Publisher: MIT Press
Total Pages: 138
Release: 2012-02-17
Genre: Architecture
ISBN: 0262516993

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!

The Golden Ratio

The Golden Ratio
Author: Gary B. Meisner
Publisher: Quarto Publishing Group USA
Total Pages: 227
Release: 2018-10-23
Genre: Mathematics
ISBN: 076036026X

This enlightening and gorgeously illustrated book explores the beauty and mystery of the divine proportion in art, architecture, nature, and beyond. From the pyramids of Giza, to quasicrystals, to the proportions of the human face, the golden ratio has an infinite capacity to generate shapes with exquisite properties. Author Gary Meisner has spent decades researching the subject, investigating and collaborating with people across the globe in dozens of professions and walks of life. In The Golden Ratio, he shares his enlightening journey. Exploring the long history of this fascinating number, as well as new insights into its power and potential applications, The Golden Ratio invites you to take a new look at this timeless topic.

A Mathematical History of the Golden Number

A Mathematical History of the Golden Number
Author: Roger Herz-Fischler
Publisher: Courier Corporation
Total Pages: 228
Release: 2013-12-31
Genre: Mathematics
ISBN: 0486152324

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.

The Golden Ratio & Fibonacci Sequence: Golden Keys to Your Genius, Health, Wealth & Excellence

The Golden Ratio & Fibonacci Sequence: Golden Keys to Your Genius, Health, Wealth & Excellence
Author: Matthew K. Cross
Publisher: Hoshin Media
Total Pages: 64
Release: 2013-04-18
Genre: Self-Help
ISBN: 9781939623003

It's been called the Secret of the Universe, a Most Precious Jewel, Nature's Path of Least Resistance and Maximum Performance and The Golden Key to the Cosmos. It is the Grand Pattern of Life, Growth and Success. It has fascinated and appears in the works of the world's greatest geniuses, including Leonardo Da Vinci, Albert Einstein, Walt Disney and Steve Jobs. Now, the open secret of the Golden Ratio and Fibonacci Sequence is revealed for your enjoyment and application. In this book you'll journey through Golden Ratio appearances and applications throughout Nature and the Universe and in all fields of human existence and endeavor, including: art, architecture, astronomy, beauty, business, culture, design, finance, health and longevity, geometry, mathematics, medicine, relationships, science and spirituality. This book presents a delightful cornucopia of Golden Ratio facts and facets, offering a bright window into its universality and power. The information presented is laser-like, with the ability to activate your unique genius and transform your consciousness. Universal wisdom will be at your fingertips once your Golden Doors of Perception are opened to the sacred design code of the Universe: The Golden Ratio & Fibonacci Sequence.

Topics in Mathematical Modeling

Topics in Mathematical Modeling
Author: Ka-Kit Tung
Publisher: Princeton University Press
Total Pages: 319
Release: 2016-06-14
Genre: Mathematics
ISBN: 1400884055

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.

Growing Patterns

Growing Patterns
Author: Sarah C. Campbell
Publisher: Astra Publishing House
Total Pages: 35
Release: 2022-07-26
Genre: Juvenile Nonfiction
ISBN: 1635928370

ALSC Notable Children's Book A wonderful introduction to one of the most beautiful connections between mathematics and the natural world–the Fibonacci sequence–through a series of stunning nature photographs. Discover the biggest mathematical mystery in nature—Fibonacci numbers! Named after a famous mathematician, the number pattern is simple and starts with: 1, 1, 2, 3, 5, 8, 13. Each number in the sequence comes from adding the two numbers before it. What's the mystery? The pattern crops up in the most unexpected places. You'll find it in the disk of a sunflower, the skin of a pineapple, and the spiral of a nautilus shell. This book brings math alive, celebrates science, and will inspire kids to see nature through new eyes.

Finding Fibonacci

Finding Fibonacci
Author: Keith Devlin
Publisher: Princeton University Press
Total Pages: 251
Release: 2017-03-07
Genre: Mathematics
ISBN: 1400885531

A compelling firsthand account of Keith Devlin's ten-year quest to tell Fibonacci's story In 2000, Keith Devlin set out to research the life and legacy of the medieval mathematician Leonardo of Pisa, popularly known as Fibonacci, whose book Liber abbaci has quite literally affected the lives of everyone alive today. Although he is most famous for the Fibonacci numbers—which, it so happens, he didn't invent—Fibonacci's greatest contribution was as an expositor of mathematical ideas at a level ordinary people could understand. In 1202, Liber abbaci—the "Book of Calculation"—introduced modern arithmetic to the Western world. Yet Fibonacci was long forgotten after his death, and it was not until the 1960s that his true achievements were finally recognized. Finding Fibonacci is Devlin's compelling firsthand account of his ten-year quest to tell Fibonacci's story. Devlin, a math expositor himself, kept a diary of the undertaking, which he draws on here to describe the project's highs and lows, its false starts and disappointments, the tragedies and unexpected turns, some hilarious episodes, and the occasional lucky breaks. You will also meet the unique individuals Devlin encountered along the way, people who, each for their own reasons, became fascinated by Fibonacci, from the Yale professor who traced modern finance back to Fibonacci to the Italian historian who made the crucial archival discovery that brought together all the threads of Fibonacci's astonishing story. Fibonacci helped to revive the West as the cradle of science, technology, and commerce, yet he vanished from the pages of history. This is Devlin's search to find him.

Fibonacci Numbers

Fibonacci Numbers
Author: Nicolai N. Vorobiev
Publisher: Birkhäuser
Total Pages: 180
Release: 2012-12-06
Genre: Mathematics
ISBN: 303488107X

Since their discovery hundreds of years ago, people have been fascinated by the wondrous properties of Fibonacci numbers. Being of mathematical significance in their own right, Fibonacci numbers have had an impact on areas like art and architecture, and their traces can be found in nature and even the behavior of the stock market. Starting with the basic properties of Fibonacci numbers, the present book explores their relevance in number theory, the theory of continued fractions, geometry and approximation theory. Rather than giving a complete account of the subject, a few chosen examples are treated exhaustively. They not only reveal the bearing of Fibonacci numbers on mathematics, but also provide very readable marvels of mathematical reasoning. This book is the translation of the 6th Russian edition (the first edition appeared in the early fifties and became a standard source of information on the subject).