Golden Number in Quantum


Book Description

"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.




Golden Number: Quantum Concepts


Book Description

"Golden Number: Quantum Concepts" is an engaging and accessible introduction to the fascinating world of quantum physics, designed for absolute beginners without a mathematical background. Through clear explanations and relatable examples, this book explores the fundamental principles of quantum mechanics, including wave-particle duality, quantum superposition, and entanglement. What sets this book apart is its unique focus on the golden ratio, a captivating mathematical constant that finds surprising connections to quantum phenomena. Readers will embark on an enlightening journey to unravel the mysteries of the quantum world while discovering the beauty of the golden ratio intertwined with quantum concepts. Whether you're a curious novice or a seeker of knowledge, this book promises to make the complexities of quantum physics accessible and engaging for all.




The Mathematics of Harmony


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."




The Golden Ratio


Book Description

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.




The Golden Section


Book Description

Tells the story of the golden section, a line segment divided into two parts such that the ratio of the short portion to the longer portion is equal to the ratio of the longer portion to the whole, and its impact on civilization and the natural world.




The Golden Number


Book Description

The first English translation of Ghyka’s masterwork on sacred geometry • Reveals how the Golden Number Phi underlies the spiritual nature of beauty and the hidden harmonies that connect the whole of creation • Explains how the spiritual mysteries of the Golden Number were passed down in an unbroken line of transmission from the Pythagorean brotherhoods through the medieval builders’ guilds to the secret societies of 18th-century Europe The Golden Number, or Phi (Φ), is a geometric ratio found throughout nature, often underlying the dimensions of objects considered especially beautiful. Simplified as 1.618 and symbolized by the Fibonacci sequence, the Golden Number represents the unique relationship within an object where the ratio of a larger part to a smaller part is the same as the ratio of the whole to the larger part. It appears in the proportions of the human face and body as well as in the proportions of animals, plants, and celestial bodies. Called the divine proportion by the monk Fra Luca Pacioli, whose book on the subject was illustrated by Leonardo da Vinci, Phi’s use in art and architecture goes back at least to the mystical mathematics of Pythagoras and his followers in the sixth century BCE. The perfect synthesis of spiritual and material, it can be found in the measurements of the sacred temples of Egypt, Ancient Greece, and Medieval and Renaissance Europe. The asymptotic series of integers that define Phi represent the macrocosm and microcosm as portrayed in Plato’s concept of the world soul. Presenting Matila Ghyka’s classic treatise on the Golden Number for the first time in English, this book reveals the many ways this ratio can be found not only in the organic forms of nature--such as in the spirals of shells or the number of petals on a flower--but also in the most beautiful and highest creations of humanity. One of the most important concepts of sacred geometry, its mysteries were passed down in an unbroken line of transmission from the Pythagorean brotherhoods through the medieval builders’ guilds to the secret societies of 18th-century Europe. Ghyka shows how the secrets of this divine proportion were not sought merely for their value in architecture, painting, and music, but also as a portal to a deeper understanding of the spiritual nature of beauty and the hidden harmonies that connect the whole of creation.




A Handbook of Number Theory in Quantum Mechanics


Book Description

"A Handbook of Number Theory in Quantum Mechanics" is a comprehensive guide designed for absolute beginners eager to explore the fascinating intersection of number theory and quantum mechanics. This book provides a clear and accessible introduction to essential concepts in both fields, from prime numbers and modular arithmetic to wave functions and quantum superposition. With step-by-step explanations, illustrative examples, and a focus on clarity, it aims to make complex topics approachable for all readers. Whether you're a student, an enthusiastic amateur, or simply curious about the mathematical foundations of the quantum world, this handbook will equip you with a solid understanding and inspire further exploration into these captivating subjects.




Number Theory in Quantum Mechanics


Book Description

"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.




The Golden Ratio And Fibonacci Numbers


Book Description

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.




The Golden Ratio


Book Description

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.