A Mathematical History Of Division In Extreme And Mean Ratio
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A Mathematical History Of Division In Extreme And Mean Ratio
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Author : Roger Herz-Fischler
language : en
Publisher: Wilfrid Laurier Univ. Press
Release Date : 1987
A Mathematical History Of Division In Extreme And Mean Ratio written by Roger Herz-Fischler and has been published by Wilfrid Laurier Univ. Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Geometry categories.
A Mathematical History Of The Golden Number
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Author : Roger Herz-Fischler
language : en
Publisher: Courier Corporation
Release Date : 2013-12-31
A Mathematical History Of The Golden Number written by Roger Herz-Fischler and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-31 with Mathematics categories.
This comprehensive study traces the historic development of division in extreme and mean ratio ("the golden number") from its first appearance in Euclid's Elements through the 18th century. Features numerous illustrations.
The Golden Ratio
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Author : Mario Livio
language : en
Publisher: Crown
Release Date : 2008-11-12
The Golden Ratio written by Mario Livio and has been published by Crown this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-12 with Mathematics categories.
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.
Companion Encyclopedia Of The History And Philosophy Of The Mathematical Sciences
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Author : Ivor Grattan-Guiness
language : en
Publisher: Routledge
Release Date : 2004-11-11
Companion Encyclopedia Of The History And Philosophy Of The Mathematical Sciences written by Ivor Grattan-Guiness and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-11 with History categories.
First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.
Proportion
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Author : Richard Padovan
language : en
Publisher: Taylor & Francis
Release Date : 2002-09-11
Proportion written by Richard Padovan and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-11 with Architecture categories.
This handbook provides the student, practising architect or interested layman with a well-illustrated and readable comparative guide to proportion systems in architecture.
In Synchrony With The Heavens Volume 2 Instruments Of Mass Calculation
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Author : David King
language : en
Publisher: BRILL
Release Date : 2005-06-01
In Synchrony With The Heavens Volume 2 Instruments Of Mass Calculation written by David King and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-01 with Philosophy categories.
This is the first investigation of one of the main interests of astronomy in Islamic civilization, namely, timekeeping by the sun and stars and the regulation of the astronomically-defined times of Muslim prayer. The study is based on over 500 medieval astronomical manuscripts first identified by the author, now preserved in libraries all over the world and originally from the entire Islamic world from the Maghrib to Central Asia and the Yemen. The materials presented provide new insights into the early development of the prayer ritual in Islam. They also call into question the popular notion that religion could not inspire serious scientific activity. Only one of the hundreds of astronomical tables discussed here was known in medieval Europe, which is one reason why the entire corpus has remained unknown until the present. A second volume, also to be published by Brill, deals with astronomical instruments for timekeeping and other computing devices.
The Golden Ratio
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Author : Gary B. Meisner
language : en
Publisher: Race Point Publishing
Release Date : 2018-10-23
The Golden Ratio written by Gary B. Meisner and has been published by Race Point Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-23 with Mathematics categories.
The Golden Ratio examines the presence of this divine number in art and architecture throughout history, as well as its ubiquity among plants, animals, and even the cosmos. This gorgeous book—with layflat dimensions that closely approximate the golden ratio—features clear, enlightening, and entertaining commentary alongside stunning full-color illustrations by Venezuelan artist and architect Rafael Araujo. 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. This book invites you to take a new look at this timeless topic, with a compilation of research and information worthy of a text book, accompanied by over 200 beautiful color illustrations that transform this into the ultimate coffee table book. Author Gary Meisner shares the results of his twenty-year investigation and collaboration with thousands of people across the globe in dozens of professions and walks of life. The evidence will close the gaps of understanding related to many claims of the golden ratio’s appearances and applications, and present new findings to take our knowledge further yet. Whoever you are, and whatever you may know about this topic, you’ll find something new, interesting, and informative in this book, and may find yourself challenged to see, apply, and share this unique number of mathematics and science in new ways.
The Golden Ratio
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Author : Francis D. Hauser, Ph.d.
language : en
Publisher: CreateSpace
Release Date : 2015-10-12
The Golden Ratio written by Francis D. Hauser, Ph.d. and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-12 with categories.
Euclid's masterpiece textbook, The Elements, was written twenty-three hundred years ago. It is primarily about geometry and contains dozens of figures. Five of these are constructed using a line that "is cut in extreme and mean ratio." Today this is called the golden ratio and is often referred to by the symbol Φ. Many myths have grown up around this ratio. This book was written to learn about them. They arise from the pyramids, the Pythagorean Brotherhood, the platonic solids, the Fibonacci numbers, sea shells, and others. There is a common thread among these myths. Φ is an irrational number (a number whose digits after the decimal point go on forever and never form a repeating pattern). Φ can be used to draw pleasing figures. But its numerical value cannot be written down using integers and fractions, which were the only numbers used in Euclid's time. Mathematicians before Euclid knew that irrational numbers existed. But to many people, a number that can't be written down was absurd. For centuries, many scientists and engineers believed that Φ was godlike. This book discusses the myths from an engineering viewpoint. The last chapter of the book shows how Euclid handled irrational numbers; how Euclid did algebra using geometry; and a simple visual proof of why there are only five platonic solids.
Mathematics And Music
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Author : Gerard Assayag
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Mathematics And Music written by Gerard Assayag and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
In Western Civilization Mathematics and Music have a long and interesting history in common, with several interactions, traditionally associated with the name of Pythagoras but also with a significant number of other mathematicians, like Leibniz, for instance. Mathematical models can be found for almost all levels of musical activities from composition to sound production by traditional instruments or by digital means. Modern music theory has been incorporating more and more mathematical content during the last decades. This book offers a journey into recent work relating music and mathematics. It contains a large variety of articles, covering the historical aspects, the influence of logic and mathematical thought in composition, perception and understanding of music and the computational aspects of musical sound processing. The authors illustrate the rich and deep interactions that exist between Mathematics and Music.
Visual Culture And Mathematics In The Early Modern Period
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Author : Ingrid Alexander-Skipnes
language : en
Publisher: Taylor & Francis
Release Date : 2017-01-06
Visual Culture And Mathematics In The Early Modern Period written by Ingrid Alexander-Skipnes and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-06 with Art categories.
During the early modern period there was a natural correspondence between how artists might benefit from the knowledge of mathematics and how mathematicians might explore, through advances in the study of visual culture, new areas of enquiry that would uncover the mysteries of the visible world. This volume makes its contribution by offering new interdisciplinary approaches that not only investigate perspective but also examine how mathematics enriched aesthetic theory and the human mind. The contributors explore the portrayal of mathematical activity and mathematicians as well as their ideas and instruments, how artists displayed their mathematical skills and the choices visual artists made between geometry and arithmetic, as well as Euclid’s impact on drawing, artistic practice and theory. These chapters cover a broad geographical area that includes Italy, Switzerland, Germany, the Netherlands, France and England. The artists, philosophers and mathematicians whose work is discussed include Leon Battista Alberti, Nicholas Cusanus, Marsilio Ficino, Francesco di Giorgio, Leonardo da Vinci and Andrea del Verrocchio, as well as Michelangelo, Galileo, Piero della Francesca, Girard Desargues, William Hogarth, Albrecht Dürer, Luca Pacioli and Raphael.