› › Mathematics Of Harmony From Euclid To Contemporary Mathematics And Computer Science

The Mathematics of Harmony

Author : Alexey Stakhov

Publisher : World Scientific

Page : 745 pages

File Size : 49,9 MB

Release : 2009

Category : Mathematics

ISBN : 9812775838

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Book Description

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."



Mathematics Of Harmony: From Euclid To Contemporary Mathematics And Computer Science

Author : Alexey Stakhov

Publisher : World Scientific

Page : 745 pages

File Size : 22,91 MB

Release : 2009-09-11

Category : Mathematics

ISBN : 9814472573

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Book Description

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 “Mathematics of Harmony,” a new interdisciplinary direction of modern science. This direction has its origins in “The Elements” 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 “golden” algebraic equations, the generalized Binet formulas, Fibonacci and “golden” 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 “golden” 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.



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

Author : Alexey Stakhov

Publisher : World Scientific

Page : 244 pages

File Size : 50,24 MB

Release : 2020-09-03

Category : Mathematics

ISBN : 9811213518

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Book Description

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.



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

Author : Alexey Stakhov

Publisher : World Scientific

Page : 247 pages

File Size : 49,11 MB

Release : 2020-05-05

Category : Mathematics

ISBN : 9811206384

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Book Description

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.



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

Author : Alexey Stakhov

Publisher : World Scientific

Page : 331 pages

File Size : 35,99 MB

Release : 2020-09-03

Category : Mathematics

ISBN : 9811213488

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Book Description

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.



"Golden" Non-euclidean Geometry, The: Hilbert's Fourth Problem, "Golden" Dynamical Systems, And The Fine-structure Constant

Author : Alexey Stakhov

Publisher : World Scientific

Page : 307 pages

File Size : 44,27 MB

Release : 2016-07-14

Category : Mathematics

ISBN : 9814678317

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Book Description

This unique book overturns our ideas about non-Euclidean geometry and the fine-structure constant, and attempts to solve long-standing mathematical problems. It describes a general theory of 'recursive' hyperbolic functions based on the 'Mathematics of Harmony,' and the 'golden,' 'silver,' and other 'metallic' proportions. Then, these theories are used to derive an original solution to Hilbert's Fourth Problem for hyperbolic and spherical geometries. On this journey, the book describes the 'golden' qualitative theory of dynamical systems based on 'metallic' proportions. Finally, it presents a solution to a Millennium Problem by developing the Fibonacci special theory of relativity as an original physical-mathematical solution for the fine-structure constant. It is intended for a wide audience who are interested in the history of mathematics, non-Euclidean geometry, Hilbert's mathematical problems, dynamical systems, and Millennium Problems.See Press Release: Application of the mathematics of harmony - Golden non-Euclidean geometry in modern math



Advances in Intelligent Systems, Computer Science and Digital Economics

Author : Zhengbing Hu

Publisher : Springer Nature

Page : 473 pages

File Size : 12,14 MB

Release : 2020-01-23

Category : Technology & Engineering

ISBN : 3030392163

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Book Description

This book comprises high-quality, refereed research papers presented at the 2019 International Symposium on Computer Science, Digital Economy and Intelligent Systems (CSDEIS2019): The symposium, held in Moscow, Russia, on 4–6 October 2019, was organized jointly by Moscow State Technical University and the International Research Association of Modern Education and Computer Science. The book discusses the state of the art in areas such as computer science and its technological applications; intelligent systems and intellectual approaches; and digital economics and methodological approaches. It is an excellent reference resource for researchers, undergraduate and graduate students, engineers, and management practitioners interested in computer science and its applications in engineering and management.



History and Philosophy of Modern Mathematics

Author : William Aspray

Publisher : U of Minnesota Press

Page : 396 pages

File Size : 40,99 MB

Release : 1988

Category : Mathematics

ISBN : 0816615675

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Book Description

History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective. The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.



The Evolution of Editorial Style in Early Modern England

Author : Jocelyn Hargrave

Publisher : Springer Nature

Page : 289 pages

File Size : 10,91 MB

Release : 2019-09-19

Category : Literary Criticism

ISBN : 3030202755

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Book Description

This book provides a historical study on the evolution of editorial style and its progress towards standardisation through an examination of early modern English style guides. The text considers the variety of ways authors, editors and printers directly implemented or uniquely interpreted and adapted the guidelines of these style guides as part of their inherently human editorial practice. Offering a critical mapping of early modern style guides, Jocelyn Hargrave explores when and how style guides originated, how they contributed to the evolution of editorial practice and how they impacted the overall publishing of content.



Decolonising Science, Technology, Engineering and Mathematics (STEM) in an Age of Technocolonialism

Author : Artwell Nhemachena

Publisher : African Books Collective

Page : 351 pages

File Size : 33,71 MB

Release : 2020-02-14

Category : Political Science

ISBN : 9956551988

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Book Description

Positing the notions of coloniality of ignorance and geopolitics of ignorance as central to coloniality and colonisation, this book examines how colonialists socially produced ignorance among colonised indigenous peoples so as to render them docile and manageable. Dismissing colonial descriptions of indigenous people as savages, illiterate, irrational, prelogical, mystical, primitive, barbaric and backward, the book argues that imperialists/colonialists contrived geopolitics of ignorance wherein indigenous regions were forced to become ignorant, hence containable and manageable in the imperial world. Questioning the provenance of modernist epistemologies, the book asks why Eurocentric scholars only contest the provenance of indigenous knowledges, artefacts and scientific collections. Interrogating why empire sponsors the decolonisation of universities/epistemologies in indigenous territories while resisting the repatriation/restitution of indigenous artefacts, the book also wonders why Westerners who still retain indigenous artefacts, skulls and skeletons in their museums, universities and private collections do not consider such artefacts and skulls to be colonising them as well. The book is valuable to scholars and activists in the fields of anthropology, museums and heritage studies, science and technology studies, decoloniality, policymaking, education, politics, sociology and development studies.