Ancient and Modern
Author: John R. Silvester
Publisher: Oxford University Press on Demand
''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.
Mathematics in History and Culture
Author: Christoph J. Scriba,Peter Schreiber
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)
Author: Charles Taylor
Publisher: Sagwan Press
Category: Juvenile Nonfiction
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
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.
Author: Charles Taylor
Publisher: Createspace Independent Publishing Platform
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.
Author: W.R. Knorr
Publisher: Springer Science & Business Media
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.
An invitation to effective thinking
Author: Edward B. Burger,Michael Starbird
Publisher: Springer Science & Business Media
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.
The History of Geometry
Author: Bonnie Leech
Publisher: The Rosen Publishing Group, Inc
Category: Juvenile Nonfiction
Introduces famous figures in the history of geometry and explains the principles that they proposed.
with a Facsimile of the First Edition
Author: René Descartes
Publisher: Courier Corporation
The great work that founded analytical geometry. Includes the original French text, Descartes' own diagrams, and the definitive Smith-Latham translation. "The greatest single step ever made in the progress of the exact sciences." — John Stuart Mill.
Author: T. A. Sarasvati Amma
Publisher: Motilal Banarsidass Publ.
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.
Author: Morris Kline
Publisher: Oxford University Press
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.
Author: Charles Dudley Warner
Publisher: Cosimo, Inc.
Popular American essayist, novelist, and journalist CHARLES DUDLEY WARNER (1829-1900) was renowned for the warmth and intimacy of his writing, which encompassed travelogue, biography and autobiography, fiction, and more, and influenced entire generations of his fellow writers. Here, the prolific writer turned editor for his final grand work, a splendid survey of global literature, classic and modern, and it's not too much to suggest that if his friend and colleague Mark Twain-who stole Warner's quip about how "everybody complains about the weather, but nobody does anything about it"-had assembled this set, it would still be hailed today as one of the great achievements of the book world. Highlights from Volume 35 include: . the poetry of Robert Southey . the verse of Edmund Spenser . the philosophy of Benedict Spinoza . the writings of Madame de Stal . the poetry of Edmund Clarence Stedman . excerpts from Laurence Sterne's Tristram Shandy . the writings of Robert Louis Stevenson . excerpts from Harriet Beecher Stowe's Uncle Tom's Cabin . and much, much more.
Author: Earl R. Anderson
Publisher: Fairleigh Dickinson Univ Press
Category: Language Arts & Disciplines
"Folk-Taxonomies in Early English is recommended for scholars and students of medieval and Renaissance English literature, for Indo-Europeanists, classicists, historical linguists, and anthropological linguists. Readers who have an interest in the philosophy of universals will be challenged by its analysis of universals as a problem in discourse analysis rather than in ontology or metaphysics."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved
Sacred Geometry, Ancient Science, and the Heavenly Order on Earth
Author: John Michell
Publisher: Simon and Schuster
Category: Body, Mind & Spirit
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.