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Geometry Through History
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Book Synopsis Geometry Civilized by : J. L. Heilbron
Download or read book Geometry Civilized written by J. L. Heilbron and published by Oxford University Press. This book was released on 2000 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A History of Non-Euclidean Geometry by : Boris A. Rosenfeld
Download or read book A History of Non-Euclidean Geometry written by Boris A. Rosenfeld and published by Springer Science & Business Media. This book was released on 2012-09-08 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis 5000 Years of Geometry by : Christoph J. Scriba
Download or read book 5000 Years of Geometry written by Christoph J. Scriba and published by Birkhäuser. This book was released on 2015-04-22 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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)
Book Synopsis History of Analytic Geometry by : Carl B. Boyer
Download or read book History of Analytic Geometry written by Carl B. Boyer and published by Courier Corporation. This book was released on 2012-06-28 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study presents the concepts and contributions from before the Alexandrian Age through to Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850. 1956 edition. Analytical bibliography. Index.
Book Synopsis Geometry by Its History by : Alexander Ostermann
Download or read book Geometry by Its History written by Alexander Ostermann and published by Springer Science & Business Media. This book was released on 2012-04-10 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which emerged in the 19thcentury. Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.
Book Synopsis The History of the Geometry Curriculum in the United States by : Nathalie Sinclair
Download or read book The History of the Geometry Curriculum in the United States written by Nathalie Sinclair and published by IAP. This book was released on 2008-02-01 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometry's Great Thinkers by : Bonnie Leech
Download or read book Geometry's Great Thinkers written by Bonnie Leech and published by The Rosen Publishing Group, Inc. This book was released on 2006-08-01 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces several mathematicians who contributed significantly to the history of geometry.
Book Synopsis Worlds Out of Nothing by : Jeremy Gray
Download or read book Worlds Out of Nothing written by Jeremy Gray and published by Springer Science & Business Media. This book was released on 2011-02-01 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the latest historical research, Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Topics covered in the first part of the book are projective geometry, especially the concept of duality, and non-Euclidean geometry. The book then moves on to the study of the singular points of algebraic curves (Plücker’s equations) and their role in resolving a paradox in the theory of duality; to Riemann’s work on differential geometry; and to Beltrami’s role in successfully establishing non-Euclidean geometry as a rigorous mathematical subject. The final part of the book considers how projective geometry rose to prominence, and looks at Poincaré’s ideas about non-Euclidean geometry and their physical and philosophical significance. Three chapters are devoted to writing and assessing work in the history of mathematics, with examples of sample questions in the subject, advice on how to write essays, and comments on what instructors should be looking for.
Download or read book Euclid's Elements written by Euclid and published by . This book was released on 2002 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book includes introductions, terminology and biographical notes, bibliography, and an index and glossary" --from book jacket.
Book Synopsis The Geometry of an Art by : Kirsti Andersen
Download or read book The Geometry of an Art written by Kirsti Andersen and published by Springer Science & Business Media. This book was released on 2008-11-23 with total page 837 pages. Available in PDF, EPUB and Kindle. Book excerpt: This review of literature on perspective constructions from the Renaissance through the 18th century covers 175 authors, emphasizing Peiro della Francesca, Guidobaldo del Monte, Simon Stevin, Brook Taylor, and Johann Heinrich. It treats such topics as the various methods of constructing perspective, the development of theories underlying the constructions, and the communication between mathematicians and artisans in these developments.
Book Synopsis Encounters with Euclid by : Benjamin Wardhaugh
Download or read book Encounters with Euclid written by Benjamin Wardhaugh and published by Princeton University Press. This book was released on 2023-11-14 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sweeping cultural history of one of the most influential mathematical books ever written Euclid's Elements of Geometry is one of the fountainheads of mathematics—and of culture. Written around 300 BCE, it has traveled widely across the centuries, generating countless new ideas and inspiring such figures as Isaac Newton, Bertrand Russell, Abraham Lincoln, and Albert Einstein. Encounters with Euclid tells the story of this incomparable mathematical masterpiece, taking readers from its origins in the ancient world to its continuing influence today. In this lively and informative book, Benjamin Wardhaugh explains how Euclid’s text journeyed from antiquity to the Renaissance, introducing some of the many readers, copyists, and editors who left their mark on the Elements before handing it on. He shows how some read the book as a work of philosophy, while others viewed it as a practical guide to life. He examines the many different contexts in which Euclid's book and his geometry were put to use, from the Neoplatonic school at Athens and the artisans' studios of medieval Baghdad to the Jesuit mission in China and the workshops of Restoration London. Wardhaugh shows how the Elements inspired ideas in theology, art, and music, and how the book has acquired new relevance to the strange geometries of dark matter and curved space. Encounters with Euclid traces the life and afterlives of one of the most remarkable works of mathematics ever written, revealing its lasting role in the timeless search for order and reason in an unruly world.
Book Synopsis The Father of Geometry by : Paul W. Hightower
Download or read book The Father of Geometry written by Paul W. Hightower and published by Enslow Publishing, LLC. This book was released on 2010-07-01 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A biography of ancient Greek mathematician Euclid, known as the father of geometry and author of the mathematics textbook Elements"--Provided by publisher.
Book Synopsis Geometry Through History by : Meighan I. Dillon
Download or read book Geometry Through History written by Meighan I. Dillon and published by Springer. This book was released on 2018-03-21 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Euclid's Window by : Leonard Mlodinow
Download or read book Euclid's Window written by Leonard Mlodinow and published by Simon and Schuster. This book was released on 2010-09-28 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other galaxy -- have been the hidden engine of the highest achievements in science and technology. Based on Mlodinow's extensive historical research; his studies alongside colleagues such as Richard Feynman and Kip Thorne; and interviews with leading physicists and mathematicians such as Murray Gell-Mann, Edward Witten, and Brian Greene, Euclid's Window is an extraordinary blend of rigorous, authoritative investigation and accessible, good-humored storytelling that makes a stunningly original argument asserting the primacy of geometry. For those who have looked through Euclid's Window, no space, no thing, and no time will ever be quite the same.
Author :Jürgen Richter-Gebert Publisher :Springer Science & Business Media ISBN 13 :3642172865 Total Pages :573 pages Book Rating :4.6/5 (421 download)
Book Synopsis Perspectives on Projective Geometry by : Jürgen Richter-Gebert
Download or read book Perspectives on Projective Geometry written by Jürgen Richter-Gebert and published by Springer Science & Business Media. This book was released on 2011-02-04 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.
Author :Bartel L. van der Waerden Publisher :Springer Science & Business Media ISBN 13 :3642617794 Total Pages :236 pages Book Rating :4.6/5 (426 download)
Book Synopsis Geometry and Algebra in Ancient Civilizations by : Bartel L. van der Waerden
Download or read book Geometry and Algebra in Ancient Civilizations written by Bartel L. van der Waerden and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally, my intention was to write a "History of Algebra", in two or three volumes. In preparing the first volume I saw that in ancient civiliza tions geometry and algebra cannot well be separated: more and more sec tions on ancient geometry were added. Hence the new title of the book: "Geometry and Algebra in Ancient Civilizations". A subsequent volume on the history of modem algebra is in preparation. It will deal mainly with field theory, Galois theory and theory of groups. I want to express my deeply felt gratitude to all those who helped me in shaping this volume. In particular, I want to thank Donald Blackmore Wagner (Berkeley) who put at my disposal his English translation of the most interesting parts of the Chinese "Nine Chapters of the Art of Arith metic" and of Liu Hui's commentary to this classic, and also Jacques Se siano (Geneva), who kindly allowed me to use his translation of the re cently discovered Arabic text of four books of Diophantos not extant in Greek. Warm thanks are also due to Wyllis Bandler (Colchester, England) who read my English text very carefully and suggested several improve ments, and to Annemarie Fellmann (Frankfurt) and Erwin Neuenschwan der (Zurich) who helped me in correcting the proof sheets. Miss Fellmann also typed the manuscript and drew the figures. I also want to thank the editorial staff and production department of Springer-Verlag for their nice cooperation.
Book Synopsis Art and Geometry by : William M. Ivins
Download or read book Art and Geometry written by William M. Ivins and published by Courier Corporation. This book was released on 2012-10-16 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This highly stimulating study observes many historical interrelationships between art and mathematics. It explores ancient and Renaissance painting and sculpture, the development of perspective, and advances in projective geometry.
