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The Mathematics Of Harmony
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Book Synopsis The Mathematics of Harmony by : Alexey Stakhov
Download or read book The Mathematics of Harmony written by Alexey Stakhov and published by World Scientific. This book was released on 2009 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."
Download or read book The Mathematics of Harmony written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Geometry of Music by : Dmitri Tymoczko
Download or read book A Geometry of Music written by Dmitri Tymoczko and published by OUP USA. This book was released on 2011-03-21 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this groundbreaking book, Tymoczko uses contemporary geometry to provide a new framework for thinking about music, one that emphasizes the commonalities among styles from Medieval polyphony to contemporary jazz.
Book Synopsis Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science-volume 3:the "Golden" Paradigm Of Modern Science: Prerequisite For The "Golden" Revolution In Mathematics,computer Science,and Theoretical Natural Sciences by : Alexey Stakhov
Download or read book Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science-volume 3:the "Golden" Paradigm Of Modern Science: Prerequisite For The "Golden" Revolution In Mathematics,computer Science,and Theoretical Natural Sciences written by Alexey Stakhov and published by World Scientific. This book was released on 2020-09-03 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume III is the third part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' 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 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction 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 generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are 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.
Download or read book Harmonograph written by Anthony Ashton and published by eBook Partnership. This book was released on 2018-04-01 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why did Pythagoras pause outside a Blacksmith's workshop? Can the nature of Harmony really be understood visually? Why do harmonies leave gaps or 'commas' when added together? In this charming little book Anthony Ashton uses a Victorian device called a Harmonograph to tell the story of Harmony and the intervals in the scale. With useful appendices and exquisite line drawings this is a unique and original introduction to this timeless subject. WOODEN BOOKS are small but packed with information. "e;Fascinating"e; FINANCIAL TIMES. "e;Beautiful"e; LONDON REVIEW OF BOOKS. "e;Rich and Artful"e; THE LANCET. "e;Genuinely mind-expanding"e; FORTEAN TIMES. "e;Excellent"e; NEW SCIENTIST. "e;Stunning"e; NEW YORK TIMES. Small books, big ideas.
Book Synopsis Hidden Harmony—Geometric Fantasies by : Umberto Bottazzini
Download or read book Hidden Harmony—Geometric Fantasies written by Umberto Bottazzini and published by Springer Science & Business Media. This book was released on 2013-06-21 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject – Cauchy, Riemann, and Weierstrass – it looks at the contributions of authors from d’Alembert to Hilbert, and Laplace to Weyl. Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.
Book Synopsis From Music to Mathematics by : Gareth E. Roberts
Download or read book From Music to Mathematics written by Gareth E. Roberts and published by JHU Press. This book was released on 2016-02-15 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guided tour of the mathematical principles inherent in music. Taking a "music first" approach, Gareth E. Roberts's From Music to Mathematics will inspire students to learn important, interesting, and at times advanced mathematics. Ranging from a discussion of the geometric sequences and series found in the rhythmic structure of music to the phase-shifting techniques of composer Steve Reich, the musical concepts and examples in the book motivate a deeper study of mathematics. Comprehensive and clearly written, From Music to Mathematics is designed to appeal to readers without specialized knowledge of mathematics or music. Students are taught the relevant concepts from music theory (notation, scales, intervals, the circle of fifths, tonality, etc.), with the pertinent mathematics developed alongside the related musical topic. The mathematics advances in level of difficulty from calculating with fractions, to manipulating trigonometric formulas, to constructing group multiplication tables and proving a number is irrational. Topics discussed in the book include • Rhythm • Introductory music theory • The science of sound • Tuning and temperament • Symmetry in music • The Bartók controversy • Change ringing • Twelve-tone music • Mathematical modern music • The Hemachandra–Fibonacci numbers and the golden ratio • Magic squares • Phase shifting Featuring numerous musical excerpts, including several from jazz and popular music, each topic is presented in a clear and in-depth fashion. Sample problems are included as part of the exposition, with carefully written solutions provided to assist the reader. The book also contains more than 200 exercises designed to help develop students' analytical skills and reinforce the material in the text. From the first chapter through the last, readers eager to learn more about the connections between mathematics and music will find a comprehensive textbook designed to satisfy their natural curiosity.
Book Synopsis Mathematics and Music by : David Wright
Download or read book Mathematics and Music written by David Wright and published by American Mathematical Soc.. This book was released on 2009 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many people intuitively sense that there is a connection between mathematics and music. If nothing else, both involve counting. There is, of course, much more to the association. David Wright's book is an investigation of the interrelationships between mathematics and music, reviewing the needed background concepts in each subject as they are encountered. Along the way, readers will augment their understanding of both mathematics and music. The text explores the common foundations of the two subjects, which are developed side by side. Musical and mathematical notions are brought together, such as scales and modular arithmetic, intervals and logarithms, tone and trigonometry, and timbre and harmonic analysis. When possible, discussions of musical and mathematical notions are directly interwoven. Occasionally the discourse dwells for a while on one subject and not the other, but eventually the connection is established, making this an integrative treatment of the two subjects. The book is a text for a freshman level college course suitable for musically inclined or mathematically inclined students, with the intent of breaking down any apprehension that either group might have for the other subject. Exercises are given at the end of each chapter. The mathematical prerequisites are a high-school level familiarity with algebra, trigonometry, functions, and graphs. Musically, the student should have had some exposure to musical staffs, standard clefs, and key signatures, though all of these are explained in the text.
Book Synopsis Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 1: The Golden Section, Fibonacci Numbers, Pascal Triangle, And Platonic Solids by : Alexey Stakhov
Download or read book Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 1: The Golden Section, Fibonacci Numbers, Pascal Triangle, And Platonic Solids written by Alexey Stakhov and published by World Scientific. This book was released on 2020-05-05 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume I is the first part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' 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 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction 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 generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are 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.
Book Synopsis Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 2: Algorithmic Measurement Theory, Fibonacci And Golden Arithmetic's And Ternary Mirror-symmetrical Arithmetic by : Alexey Stakhov
Download or read book Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 2: Algorithmic Measurement Theory, Fibonacci And Golden Arithmetic's And Ternary Mirror-symmetrical Arithmetic written by Alexey Stakhov and published by World Scientific. This book was released on 2020-09-03 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume II is the second part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' 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 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction 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 generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are 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.
Book Synopsis Music: A Mathematical Offering by : Dave Benson
Download or read book Music: A Mathematical Offering written by Dave Benson and published by Cambridge University Press. This book was released on 2007 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the interaction between music and mathematics including harmony, symmetry, digital music and perception of sound.
Book Synopsis A History of Mathematics by : Carl B. Boyer
Download or read book A History of Mathematics written by Carl B. Boyer and published by John Wiley & Sons. This book was released on 2011-01-11 with total page 695 pages. Available in PDF, EPUB and Kindle. Book excerpt: The updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincaré Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs. Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments. Whether you're interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.
Download or read book Harmony Book written by Elliott Carter and published by Carl Fischer, L.L.C.. This book was released on 2002 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive resource features more than 400 projections and colour illustrations augmented by MRI images for added detail to enhance the anatomy and positioning presentations.
Book Synopsis Elements of Point Set Topology by : John D. Baum
Download or read book Elements of Point Set Topology written by John D. Baum and published by Courier Corporation. This book was released on 1991-01-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.
Book Synopsis Mathematics and Music by : James S. Walker
Download or read book Mathematics and Music written by James S. Walker and published by CRC Press. This book was released on 2013-04-10 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: At first glance, mathematics and music seem to be from separate worlds—one from science, one from art. But in fact, the connections between the two go back thousands of years, such as Pythagoras’s ideas about how to quantify changes of pitch for musical tones (musical intervals). Mathematics and Music: Composition, Perception, and Performance explores the many links between mathematics and different genres of music, deepening students’ understanding of music through mathematics. In an accessible way, the text teaches the basics of reading music and explains how various patterns in music can be described with mathematics. The authors extensively use the powerful time-frequency method of spectrograms to analyze the sounds created in musical performance. Numerous examples of music notation assist students in understanding basic musical scores. The text also provides mathematical explanations for musical scales, harmony, and rhythm and includes a concise introduction to digital audio synthesis. Along with helping students master some fundamental mathematics, this book gives them a deeper appreciation of music by showing how music is informed by both its mathematical and aesthetic structures. Web Resource On the book’s CRC Press web page, students can access videos of many of the spectrograms discussed in the text as well as musical scores playable with the free music software MuseScore. An online bibliography offers many links to free downloadable articles on math and music. The web page also provides links to other websites related to math and music, including all the sites mentioned in the book.
Book Synopsis The Harmony of the World by : Johannes Kepler
Download or read book The Harmony of the World written by Johannes Kepler and published by American Philosophical Society. This book was released on 1997 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors have presented and interpreted Johannes Kepler's Latin text to English readers by putting it into the kind of clear but earnest language they suppose Kepler would have used if he had been writing today.
Book Synopsis Mathematical Omnibus by : D. B. Fuks
Download or read book Mathematical Omnibus written by D. B. Fuks and published by American Mathematical Soc.. This book was released on 2007 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.
