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| Author | : Charles B. Madden |
| Publisher | : |
| Total Pages | : 366 |
| Release | : 2005 |
| Genre | : Music |
| ISBN | : 9780967172767 |
This study of the use of the golden proportion in classical music shows that 53 of the 70 composers studied used it to structure their works, some of them knowingly. Since this is seldom discussed in courses in music theory, this book should be a major contribution to our understanding of musical structure.
| Author | : Charles B. Madden |
| Publisher | : High Art Press |
| Total Pages | : 228 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 9780967172750 |
Fractals in Music is intended for advanced students of music theory, whether individuals, composers, students, or teachers. It is intelligible to anyone having some knowledge of algebra and trigonometry. The many illustrations clarify such concepts as self-similarity and transforms. Book jacket.
| 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.
| Author | : Thomas Koshy |
| Publisher | : OUP USA |
| Total Pages | : 439 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 019533454X |
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 | : Bill Manaris |
| Publisher | : CRC Press |
| Total Pages | : 496 |
| Release | : 2014-05-19 |
| Genre | : Computers |
| ISBN | : 1482222213 |
Teach Your Students How to Use Computing to Explore Powerful and Creative IdeasIn the twenty-first century, computers have become indispensable in music making, distribution, performance, and consumption. Making Music with Computers: Creative Programming in Python introduces important concepts and skills necessary to generate music with computers.
| Author | : Alfred S. Posamentier |
| Publisher | : Prometheus Books |
| Total Pages | : 385 |
| Release | : 2010-12-30 |
| Genre | : Mathematics |
| ISBN | : 1615920226 |
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.
| Author | : Constance Brown |
| Publisher | : John Wiley & Sons |
| Total Pages | : 208 |
| Release | : 2010-05-13 |
| Genre | : Business & Economics |
| ISBN | : 0470883243 |
Only someone who is both a successful trader and a successful writer could pull off what Constance Brown has accomplished in this book: distilling Fibonacci analysis to two hundred or so comprehensive, clearly written, eminently practical pages. Brown knows exactly what a professional trying to come up to speed on a new trading tool needs and she provides it, covering what Fibonacci analysis is, how it works, where it comes from, pitfalls and dangers, and, of course, how to use it. Basic trading strategies are touched upon in virtually every chapter. Fibonacci analysis is one of the most popular technical analysis tools, yet it is often used incorrectly. Brown quickly clears up common misconceptions and moves on to show, step by step, the correct way to apply the technique in any market. Those with Fibonacci analysis software will learn how to use it with maximum effectiveness; those without will chart the market the old-fashioned way. All will find answers to the trader's most important questions: Where is the market going? At what level should my stop be entered? Based on the size of my trading account, how much should I leverage into a trading position? Can I tell if I am in trouble before my stop is hit? How much should I buy or sell if given a second or third opportunity? Occasional references to other tools--including Elliott Wave, W.D. Gann, and candlestick charts--and an extensive bibliography make this book richer for accomplished technical analysts without confounding the less experienced. Plentiful real-life examples and dozens of carefully annotated charts insure every reader will get maximum value from every minute spent with this book. Gold Medal Winner (tie), Investing Category, Axiom Business Book Awards (2009) Winner: Book Series Cover Design, The Bookbinders Guild of New York/2009 New York Book Show Awards
| 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.
| Author | : Alexey Stakhov |
| Publisher | : World Scientific |
| Total Pages | : 745 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 9812775838 |
Assisted by Scott Olsen ( Central Florida Community College, USA ). This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the OC Mathematics of Harmony, OCO a new interdisciplinary direction of modern science. This direction has its origins in OC The ElementsOCO of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the OC goldenOCO algebraic equations, the generalized Binet formulas, Fibonacci and OC goldenOCO matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and OC goldenOCO matrices). The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Sample Chapter(s). Introduction (503k). Chapter 1: The Golden Section (2,459k). Contents: Classical Golden Mean, Fibonacci Numbers, and Platonic Solids: The Golden Section; Fibonacci and Lucas Numbers; Regular Polyhedrons; Mathematics of Harmony: Generalizations of Fibonacci Numbers and the Golden Mean; Hyperbolic Fibonacci and Lucas Functions; Fibonacci and Golden Matrices; Application in Computer Science: Algorithmic Measurement Theory; Fibonacci Computers; Codes of the Golden Proportion; Ternary Mirror-Symmetrical Arithmetic; A New Coding Theory Based on a Matrix Approach. Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science."
| 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.
