Search Results: geometry-ancient-and-modern

Geometry

Ancient and Modern

Author: John R. Silvester

Publisher: Oxford University Press on Demand

ISBN: 9780198508250

Category: Mathematics

Page: 313

View: 9521

''This book is densely packed with useful and interesting geometrical insights whilst the written style is engaging and often amusing... John Silvester has written a work of quality and substance and I strongly recommended it for use by anyone seeking to extend their knowledge of geometry beyond the A level stage. As one who is intrigued by geometry, I shall certainly keep my copy permanently close to hand'' -The Mathematical GazetteThis book offers a guided tour of geometry from euclid through to algebraic geometry. It shows how mathematicians use a variety of techniques to tackle problems , and it links geometry to other branches of mathematics. Many problems and examples are included to aid understanding.

5000 Years of Geometry

Mathematics in History and Culture

Author: Christoph J. Scriba,Peter Schreiber

Publisher: Birkhäuser

ISBN: 3034808984

Category: Mathematics

Page: 626

View: 6658

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)

An Introduction to the Ancient and Modern Geometry of Conics Being a Geometrical Treatise on the Conic Sections with a Collection of Problems and Historical Notes and Prolegomena

Author: Charles Taylor

Publisher: Createspace Independent Publishing Platform

ISBN: 9781523930067

Category:

Page: 472

View: 7490

An Introduction to the Ancient and Modern Geometry of Conics Being a Geometrical Treatise on the Conic Sections with a Collection of Problems and Historical Notes and Prolegomena by Charles Taylor. This book is a reproduction of the original book published in 1881 and may have some imperfections such as marks or hand-written notes.

Geometry's Great Thinkers

The History of Geometry

Author: Bonnie Leech

Publisher: The Rosen Publishing Group, Inc

ISBN: 9781404260733

Category: Juvenile Nonfiction

Page: 32

View: 7483

Introduces famous figures in the history of geometry and explains the principles that they proposed.

Popular Science

Author: N.A

Publisher: N.A

ISBN: N.A

Category:

Page: 112

View: 2570

Popular Science gives our readers the information and tools to improve their technology and their world. The core belief that Popular Science and our readers share: The future is going to be better, and science and technology are the driving forces that will help make it better.

Textual Studies in Ancient and Medieval Geometry

Author: W.R. Knorr

Publisher: Springer Science & Business Media

ISBN: 9780817633875

Category: Mathematics

Page: 864

View: 8164

For textual studies relating to the ancient mathematical corpus the efforts by the Danish philologist, 1. L. Heiberg (1854-1928), are especially significant. Beginning with his doctoral dissertation, Quaestiones Archimedeae (Copen hagen, 1879), Heiberg produced an astonishing series of editions and critical studies that remain the foundation of scholarship on Greek mathematical 4 science. For comprehensiveness and accuracy, his editions are exemplary. In his textual studies, as also in the prolegomena to his editions, he carefully described the extant evidence, organized the manuscripts into stemmata, and drew out the implications for the state of the text. 5 With regard to his Archimedean work, Heiberg sometimes betrayed signs of the philologist's occupational disease - the tendency to rewrite a text deemed on subjective grounds to be unworthy. 6 But he did so less often than his prominent 7 contemporaries, and not as to detract appreciably from the value of his editions. In examining textual questions bearing on the Archimedean corpus, he attempted to exploit as much as possible evidence from the ancient commentators, and in some instances from the medieval translations. It is here that opportunities abound for new work, extending, and in some instances superseding, Heiberg's findings. For at his time the availability of the medieval materials was limited. In recent years Marshall Clagett has completed a mammoth critical edition of the medieval Latin tradition of Archimedes,8 while the bibliographical instruments for the Arabic tradition are in good order thanks to the work of Fuat Sezgin.

Mathematical Thought From Ancient to Modern Times

Author: Morris Kline

Publisher: Oxford University Press

ISBN: 9780199840434

Category: Mathematics

Page: 448

View: 4398

This comprehensive history traces the development of mathematical ideas and the careers of the men responsible for them. Volume 1 looks at the disciplines origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.

Geometry in Ancient and Medieval India

Author: T. A. Sarasvati Amma

Publisher: Motilal Banarsidass Publ.

ISBN: 9788120813441

Category: Geometry

Page: 277

View: 8942

This book is a geometrical survey of the Sanskrit and Prakrt scientific and quasi-scientific literature of India, beginning with the Vedic literature and ending with the early part of the 17th century. It deals in detail with the Sulbasutras in the Vedic literature, with the mathematical parts of Jaina Canonical works and of the Hindu Siddhantas and with the contributions to geometry made by the astronomer mathematicians Aryabhata I & II, Sripati, Bhaskara I & II, Sangamagrama Madhava, Paramesvara, Nilakantha, his disciples and a host of others. The works of the mathematicians Mahavira, Sridhara and Narayana Pandita and the Bakshali Manuscript have also been studied. The work seeks to explode the theory that the Indian mathematical genius was predominantly algebraic and computational and that it eschewed proofs and rationales. There was a school in India which delighted to demonstrate even algebraical results geometrically. In their search for a sufficiently good approximation for the value of pie Indian mathematicians had discovered the tool of integration. Which they used equally effectively for finding the surface area and volume of a sphere and in other fields. This discovery of integration was the sequel of the inextricable blending of geometry and series mathematics.

An Introduction to the Ancient and Modern Geometry of Conics

Being a Geometrical Treatise on the Conic Sections with a Collection of Problems and Historical Notes and Prolegomena

Author: Charles Taylor

Publisher: N.A

ISBN: N.A

Category: Conic sections

Page: 384

View: 4577

The Heart of Mathematics

An invitation to effective thinking

Author: Edward B. Burger,Michael Starbird

Publisher: Springer Science & Business Media

ISBN: 9781931914413

Category: Mathematics

Page: 760

View: 1607

Hallmark features include: * A focus on the important ideas of mathematics that students will retain long after their formal studies are complete. * An engaging and humorous style, written to be read and enjoyed. * Ten Life Lessons that readers will apply beyond their study of mathematics. * Use of a variety of visualization techniques that direct students to model their thinking and to actively explore the world around them. New to this Edition: * A new chapter, Deciding Wisely: Applications of Rigorous Thought, provides a thought-provoking capstone. * Expanded and improved statistics and probability content in Chapter 7, Taming Uncertainty. * Enhanced Mindscapes at the end of each section which ask the reader to review, apply and think deeply about the ideas presented in the chapter. * Radically superior ancillary package.

5000 Jahre Geometrie

Geschichte Kulturen Menschen

Author: Christoph J. Scriba,Peter Schreiber

Publisher: Springer-Verlag

ISBN: 3662045001

Category: Mathematics

Page: 596

View: 8665

Lange bevor die Schrift entwickelt wurde, hat der Mensch geometrische Strukturen wahrgenommen und systematisch verwendet: ob beim Weben oder Flechten einfacher zweidimensionaler Muster oder beim Bauen mit dreidimensionalen Körpern. Das Buch liefert einen faszinierenden Überblick über die geometrischen Vorstellungen und Erkenntnisse der Menschheit von der Urgesellschaft bis hin zu den mathematischen und künstlerischen Ideen des 20. Jahrhunderts.

The Dimensions of Paradise

Sacred Geometry, Ancient Science, and the Heavenly Order on Earth

Author: John Michell

Publisher: Simon and Schuster

ISBN: 159477773X

Category: Body, Mind & Spirit

Page: 256

View: 9960

An in-depth look at the role of number as a bridge between Heaven and Earth • Reveals the numerical code by which the ancients maintained high standards of art and culture • Sets out the alchemical formulas for the fusion of elements and the numerical origins of various sacred names and numbers • Describes the rediscovery of knowledge associated with the Holy Grail, through which the influence of the Heavenly Order is made active on Earth The priests of ancient Egypt preserved a geometrical canon, a numerical code of harmonies and proportions, that they applied to music, art, statecraft, and all the institutions of their civilization. Plato, an initiate in the Egyptian mysteries, said it was the instrument by which the ancients maintained high, principled standards of civilization and culture over thousands of years. In The Dimensions of Paradise, John Michell describes the results of a lifetime’s research, demonstrating how the same numerical code underlies sacred structures from ancient times to the Christian era. In the measurements of Stonehenge, the foundation plan of Glastonbury, Plato’s ideal city, and the Heavenly City of the New Jerusalem described in the vision of Saint John lie the science and cosmology on which the ancient world order was founded. The central revelation of this book is a structure of geometry and number representing the essential order of the heavens and functioning as a map of paradise.

A Summary of Geography and History both ancient and modern. With maps

Author: Alexander ADAM (LL.D.)

Publisher: N.A

ISBN: N.A

Category:

Page: 858

View: 9350

Art and Geometry

A Study in Space Intuitions

Author: William M. Ivins

Publisher: Courier Corporation

ISBN: 0486143589

Category: Art

Page: 128

View: 6866

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.

Old and New Unsolved Problems in Plane Geometry and Number Theory

Author: Victor Klee,Stan Wagon

Publisher: Cambridge University Press

ISBN: 9780883853153

Category: Mathematics

Page: 333

View: 5097

This book discusses 24 unsolved problems in number theory and geometry.

Famous Problems of Geometry and How to Solve Them

Author: Benjamin Bold

Publisher: Courier Corporation

ISBN: 0486137635

Category: Science

Page: 144

View: 367

Delve into the development of modern mathematics and match wits with Euclid, Newton, Descartes, and others. Each chapter explores an individual type of challenge, with commentary and practice problems. Solutions.

Concepts of Space, Ancient and Modern

Author: Kapila Vatsyayan

Publisher: Abhinav Publications

ISBN: 8170172527

Category: Philosophy

Page: 665

View: 9692

Geometry Civilized

History, Culture, and Technique

Author: J. L. Heilbron

Publisher: Oxford University Press

ISBN: 9780198506904

Category: Mathematics

Page: 309

View: 3096

Geometry Civilized is a unique combination of history and mathematics. It contains a full introduction to plane geometry and trigonometry within a fascinating historical framework that sets off the technical material. This approach to geometrical ideas gives the book its unique, readable style. The author has included a wide range of unusual and engaging geometric problems, many of which are taken from practical applications, drawn from sources ranging from ancient to modern. The study of geometry has been an important element of education in Europe since the time of the Greeks. This book helps us to understand why such emphasis has been placed on obtaining a good understanding of geometry. But the history presented here is not confined to the Western tradition. Examples drawn from other cultures, particularly Chinese and Indian, underscore the peculiarities of the geometry we have inherited from the Greeks, and thereby make Euclid's approach more accessible. Book reviews from the hardback: 'He has written a marvellous tale of how, throughout much of recorded history, geometrical thinking and civilisation have been closely intertwined. ...Definitely a book to dip into and reflect on a superior form of brainfood for the beach this summer perhaps? Heilbron's enthusiasm is contagious.' Ian Stewart, New Scientist 'The book is wonderfully illustrated. There are diagrams on almost every page, apt illustrations from older books, and well chosen photographs,together with eight colour plates. The appearance of the book is quite seductive, for which Oxford University Press should be congratulated.' Jeremy Gray, Nature 'This is a handsome book, well researched and entertainingly written. It shows how powerfully a historically informed account can communicate. If you thought Euclidean geometry was something only your great-grandparents did - try it, you will be surprised.' BJune Barrow-Green, The TIMES Higher Education Supplement

Geometry Through History

Euclidean, Hyperbolic, and Projective Geometries

Author: Meighan I. Dillon

Publisher: Springer

ISBN: 3319741357

Category: Mathematics

Page: 350

View: 7274

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.

The Philosophy of Mathematics

Translated from Cours de Philosophie Positive by W. M. Gillespie

Author: Auguste Comte

Publisher: Courier Corporation

ISBN: 0486155137

Category: Mathematics

Page: 272

View: 6519

Written by the nineteenth-century French philosophical founder of positivism, this comprehensive map of mathematical science assigns to each part of the complex whole its true position and value.

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