The Golden Ratio And Fibonacci Numbers

The Golden Ratio And Fibonacci Numbers
Author: Richard A Dunlap
Publisher: World Scientific
Total Pages: 170
Release: 1997-12-16
Genre: Mathematics
ISBN: 9814496944

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 Number

The Golden Number
Author: Matila C. Ghyka
Publisher: Inner Traditions
Total Pages: 448
Release: 2016-10-30
Genre: Body, Mind & Spirit
ISBN: 9781594771002

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.

Pup's Numbers

Pup's Numbers
Author: Amye Rosenberg
Publisher: Golden Press
Total Pages: 10
Release: 1986
Genre: Board books
ISBN: 9780307123084

With one pair of scissors, two brushes, three jars of paint, four balls of yarn, and five crayons Pup makes six birds, seven monster masks, eight elephants, and nine pigs, while his mother makes him ten cookies

The Book of Numbers

The Book of Numbers
Author: Tim Glynne-Jones
Publisher: Arcturus Publishing
Total Pages: 310
Release: 2011-06-30
Genre: Mathematics
ISBN: 1848584407

From zero to infinity, The Book of Numbers is a handy-sized volume which opens up a new realm of knowledge. Where else in one place could you find out how the illegal numbers racket worked, what makes some people see numbers as colours, why the standard US rail gauge exactly matches the axle width of an ancient Roman chariot, and the numerological connection between Adolf Hitler and Osama Bin Laden?

1750-1755

1750-1755
Author: Royal Society (Great Britain)
Publisher:
Total Pages: 768
Release: 1809
Genre: Science
ISBN:

Encyclopaedia of Historical Metrology, Weights, and Measures

Encyclopaedia of Historical Metrology, Weights, and Measures
Author: Jan Gyllenbok
Publisher: Birkhäuser
Total Pages: 691
Release: 2018-04-11
Genre: Science
ISBN: 3319575988

This first of three volumes starts with a short introduction to historical metrology as a scientific discipline and goes on with an anthology of acient and modern measurement systems of all kind, scientific measures, units of time, weights, currencies etc. It concludes with an exhaustive list of references. Units of measurement are of vital importance in every civilization through history. Since the early ages, man has through necessity devised various measures to assist him in everyday life. They have enabled and continue to enable us to trade in commonly and equitably understood amounts, and to investigate, understand, and control the chemical, physical, and biological processes of the natural world. The essence of the work is an alphabetically ordered, comprehensive list of measurement nomenclature, units and scales. It provides an understanding of almost all quantitative expressions observed in all imaginable situations, including spelling variants and the abbreviations and symbols for units, and various acronyms used in metrology. It will be of use not only to historians of science and technology, but also to economic and social historians and should be in every major academic and national library as standard reference work on the topic.

Fibonacci Numbers

Fibonacci Numbers
Author: Nicolai N. Vorobiev
Publisher: Birkhäuser
Total Pages: 180
Release: 2012-12-06
Genre: Mathematics
ISBN: 303488107X

Since their discovery hundreds of years ago, people have been fascinated by the wondrous properties of Fibonacci numbers. Being of mathematical significance in their own right, Fibonacci numbers have had an impact on areas like art and architecture, and their traces can be found in nature and even the behavior of the stock market. Starting with the basic properties of Fibonacci numbers, the present book explores their relevance in number theory, the theory of continued fractions, geometry and approximation theory. Rather than giving a complete account of the subject, a few chosen examples are treated exhaustively. They not only reveal the bearing of Fibonacci numbers on mathematics, but also provide very readable marvels of mathematical reasoning. This book is the translation of the 6th Russian edition (the first edition appeared in the early fifties and became a standard source of information on the subject).