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"Golden Harmony: Quantum Numbers" delves into the intricate world of quantum mechanics, exploring the concept of quantum numbers with a focus on their profound significance and application in understanding the behavior of subatomic particles. Through accessible explanations and engaging examples, the book navigates readers through the fascinating realm of quantum physics, shedding light on the fundamental principles that govern the quantum world and highlighting the beauty and harmony inherent in its mathematical framework.
Number Theory in Quantum Mechanics by N.B. Singh Pdf
"Number Theory in Quantum Mechanics" is a specialized exploration that bridges the realms of number theory and quantum mechanics. Catering to students, physicists, and researchers in quantum physics, this book investigates the intriguing connections between number theory concepts and quantum phenomena. Covering topics such as quantum states, operators, and wave functions, the book illuminates the mathematical underpinnings that emerge when applying number theory principles to quantum mechanics. With clarity and depth, this book serves as a valuable resource for those intrigued by the intersection of mathematical theory and quantum physics, offering new perspectives on the fundamental nature of quantum systems.
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.
Author : Gary B. Meisner Publisher : Quarto Publishing Group USA Page : 227 pages File Size : 55,7 Mb Release : 2018-10-23 Category : Mathematics ISBN : 9780760360262
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.
What was the golden secret known to Leonardo da Vinci, Kepler, Plato and the ancient magicians? Can there really be a key to nature and life itself? In this small but compact volume internationally renowned divine proportion supersleuth Dr Olsen unravels perhaps the greatest mystery of all time, a code that seems to underly life, the universe and everything, a pattern we instinctively recognise as beautiful, and which nature herself uses at every scale. Designed for artists and scientists alike, this is the smallest, densest and most beautiful book on the golden section ever produced. 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.
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."
Numbers, operators, and degrees of independence facilitate creation and organization of the real environment. The explanation and application of quantum mechanics on atomic and cosmic scales is suggested by the Pythagorean tradition
Quantum Of Time: Transformations by Mayukh Maitra Pdf
: The book provides comprehensive details on the state transition for a system by transformations, using the Golden ratio, as invariable over finite distances in the quantum of time.
Electronic Structure and Number Theory by Jan C.A. Boeyens,Peter Comba Pdf
The series Structure and Bonding publishes critical reviews on topics of research concerned with chemical structure and bonding. The scope of the series spans the entire Periodic Table and addresses structure and bonding issues associated with all of the elements. It also focuses attention on new and developing areas of modern structural and theoretical chemistry such as nanostructures, molecular electronics, designed molecular solids, surfaces, metal clusters and supramolecular structures. Physical and spectroscopic techniques used to determine, examine and model structures fall within the purview of Structure and Bonding to the extent that the focus is on the scientific results obtained and not on specialist information concerning the techniques themselves. Issues associated with the development of bonding models and generalizations that illuminate the reactivity pathways and rates of chemical processes are also relevant. The individual volumes in the series are thematic. The goal of each volume is to give the reader, whether at a university or in industry, a comprehensive overview of an area where new insights are emerging that are of interest to a larger scientific audience. Thus each review within the volume critically surveys one aspect of that topic and places it within the context of the volume as a whole. The most significant developments of the last 5 to 10 years should be presented using selected examples to illustrate the principles discussed. A description of the physical basis of the experimental techniques that have been used to provide the primary data may also be appropriate, if it has not been covered in detail elsewhere. The coverage need not be exhaustive in data, but should rather be conceptual, concentrating on the new principles being developed that will allow the reader, who is not a specialist in the area covered, to understand the data presented. Discussion of possible future research directions in the area is welcomed.
The Mathematics of Harmony by Alekse? Petrovich Stakhov,Scott Anthony Olsen Pdf
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.
Author : Arthur I Miller Publisher : W. W. Norton & Company Page : 388 pages File Size : 41,5 Mb Release : 2009-03-24 Category : History ISBN : 9780393065329
Deciphering the Cosmic Number by Arthur I Miller Pdf
The extraordinary story of psychoanalyst Carl Jung and physicist Wolfgang Pauli and their struggle to quantify the unconscious. In 1932, the groundbreaking physicist Wolfgang Pauli met the famous psychoanalyst Carl Jung. Pauli was fascinated by the inner reaches of his own psyche and not afraid to dabble in the occult, while Jung looked to science for answers to the psychological questions that tormented him. Their rich friendship led them, in Jung’s words, into “the no-man’s land between physics and the psychology of the unconscious . . . the most fascinating yet the darkest hunting ground of our times.” Both were obsessed with the far-reaching significance of the number “137”—a primal number that seemed to hint at the origins of the universe itself. Their quest to solve its enigma led them on a lifelong journey into the ancient secrets of alchemy, the work of Johannes Kepler, and the Chinese Book of Changes. This is the captivating story of an extraordinary and fruitful collaboration between two of the greatest thinkers of the twentieth century.
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.
Mendeleev to Oganesson by Eric R. Scerri,Guillermo Restrepo Pdf
An edited volume featuring chapters on multidisciplinary aspects of the Periodic Table, particularly focusing on the history and philosophy of chemistry.