Geometry Through History
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Geometry Through History
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Author : Meighan I. Dillon
language : en
Publisher: Springer
Release Date : 2018-03-21
Geometry Through History written by Meighan I. Dillon and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-21 with Mathematics categories.
Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the field.
Geometry Through History
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Author : Meighan Dillon
language : en
Publisher:
Release Date : 2018
Geometry Through History written by Meighan Dillon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Geometry categories.
Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid's system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid's work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the field.--
5000 Years Of Geometry
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Author : Christoph J. Scriba
language : en
Publisher: Birkhäuser
Release Date : 2015-04-22
5000 Years Of Geometry written by Christoph J. Scriba and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-22 with Mathematics categories.
The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book “5000 Jahre Geometrie,” in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science and engineering. Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries. Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometr y in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times. The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history. From letters to the authors for the German language edition I hope it gets a translation, as there is no comparable work. Prof. J. Grattan-Guinness (Middlesex University London) "Five Thousand Years of Geometry" - I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically! Prof. J.W. Dauben (City University of New York) An excellent book in every respect. The authors have successfully combined the history of geometry with the general development of culture and history. ... The graphic design is also excellent. Prof. Z. Nádenik (Czech Technical University in Prague)
A History Of Non Euclidean Geometry
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Author : Boris A. Rosenfeld
language : en
Publisher: Springer
Release Date : 1988-09-07
A History Of Non Euclidean Geometry written by Boris A. Rosenfeld and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-09-07 with Mathematics categories.
The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. " During the seventies of the last century there occurred another scientific revolution. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility, to the arithmetics and algebras of many groups and fields in addition to the arith metic and algebra of real and complex numbers, and, finally, to new mathe matical systems, i. e. , sets furnished with various structures having no classical analogues. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe matics.
Geometry In History
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Author : S. G. Dani
language : en
Publisher: Springer Nature
Release Date : 2019-10-18
Geometry In History written by S. G. Dani and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-18 with Mathematics categories.
This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.
The History Of The Geometry Curriculum In The United States
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Author : Nathalie Sinclair
language : en
Publisher: IAP
Release Date : 2008-02-01
The History Of The Geometry Curriculum In The United States written by Nathalie Sinclair and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-01 with Education categories.
This volume investigates the evolution of the geometry curriculum in the United States over the past 150 years. A primary goal is to increase awareness of the shape and nature of the current geometry curriculum by explaining how things have come to be as they are. Given the limited access to first-hand accounts of the enacted geometry curriculum during the past 150 years, the monograph relies on textbooks to provide a record of the implemented curriculum at any given point in time. Policy documents can provide insight into the choices made in textbooks by hinting at the issues considered and the recommendations made. The monograph is organized in a chronological sequence of "notable events" leading to discernable changes in thinking about the geometry curriculum over the past century and a half—roughly the extent of time during which geometry has been taught in American schools. Notable events include important reports or commissions, influential texts, new schools of thought, and developments in learning technologies. These events affected, among other things: content and aims of the geometry curriculum; the nature of mathematical activity as construed by both mathematicians and mathematics educators; and, the resources students are given for engaging in mathematical activity. Before embarking through the notable events, it is necessary to consider the "big bang" of geometry, namely the moment in time that shaped the future life of the geometry curriculum. This corresponds to the emergence of Euclidean geometry. Given its influence on the shape of the geometry curriculum, familiarity with the nature of the geometry articulated in Euclid’s Elements is essential to understanding the many tensions that surround the school geometry curriculum. Several themes emerge over the course of the monograph, and include: the aims and means of the geometry curriculum, the importance of proof in geometry, the role of visualization and tactile experiences, the fusion between solid and plane geometry, the curricular connections between geometry and algebra, and the use of motion and continuity. The intended audience would include curriculum developers, researchers, teachers, and curriculum supervisors.
Non Euclidean Geometry
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Author : Roberto Bonola
language : en
Publisher: Courier Corporation
Release Date : 1955-01-01
Non Euclidean Geometry written by Roberto Bonola and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1955-01-01 with Mathematics categories.
Examines various attempts to prove Euclid's parallel postulate — by the Greeks, Arabs and Renaissance mathematicians. Ranging through the 17th, 18th, and 19th centuries, it considers forerunners and founders such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss, Schweikart, Taurinus, J. Bolyai and Lobachewsky. Includes 181 diagrams.
A History Of Geometrical Methods
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Author : Julian Lowell Coolidge
language : en
Publisher: Courier Corporation
Release Date : 2013-02-27
A History Of Geometrical Methods written by Julian Lowell Coolidge and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-27 with Mathematics categories.
Full and authoritative, this history of the techniques for dealing with geometric questions begins with synthetic geometry and its origins in Babylonian and Egyptian mathematics; reviews the contributions of China, Japan, India, and Greece; and discusses the non-Euclidean geometries. Subsequent sections cover algebraic geometry, starting with the precursors and advancing to the great awakening with Descartes; and differential geometry, from the early work of Huygens and Newton to projective and absolute differential geometry. The author's emphasis on proofs and notations, his comparisons between older and newer methods, and his references to over 600 primary and secondary sources make this book an invaluable reference. 1940 edition.
Geometry S Great Thinkers
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Author : Bonnie Leech
language : en
Publisher: The Rosen Publishing Group, Inc
Release Date : 2006-08-01
Geometry S Great Thinkers written by Bonnie Leech and has been published by The Rosen Publishing Group, Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-01 with Juvenile Nonfiction categories.
This book introduces students to both ancient and modern pioneer figures of geometry. Students are entertainingly guided through important theories and concepts integral to the use of geometry. Includes detailed background information on Pythagoras of Samos, Euclid of Alexandria, Rene Descartes, and Grace Chisholm Young. Fascinating coverage is provided on the models of the Pythagorean theorem, the basics of Euclidean geometry, and the Cartesian coordinate system.
Geometry Civilized
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Author : J. L. Heilbron
language : en
Publisher: Oxford University Press
Release Date : 2000
Geometry Civilized written by J. L. Heilbron and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with History categories.
This lavishly illustrated book provides an unusually accessible approach to geometry by placing it in historical context. With concise discussions and carefully chosen illustrations the author brings the material to life by showing what problems motivated early geometers throughout the world. Geometry Civilized covers classical plane geometry, emphasizing the methods of Euclid but also drawing on advances made in China and India. It includes a wide range of problems, solutions, and illustrations, as well as a chapter on trigonometry, and prepares its readers for the study of solid geometry and conic sections.