The Geometry of René Descartes

with a Facsimile of the First Edition

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Author: René Descartes

Publisher: Courier Corporation

ISBN: 0486158179

Category: Mathematics

Page: 272

View: 8470

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.

Argumentieren mit multiplen und dynamischen Repräsentationen

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Author: Andreas Bauer

Publisher: BoD – Books on Demand

ISBN: 3958260225

Category: Mathematics

Page: 132

View: 9853

Kaum eine mathematische Tätigkeit bestimmt das Wesen der Mathematik so sehr wie das Argumentieren. Dies gilt gleichermaßen für den Mathematikunterricht in der Sekundarstufe. Wer argumentiert, benötigt jedoch Informationen, um Aussagen formulieren zu können. Diese werden in der Mathematik durch Repräsentationen mathematischer Objekte bereitgestellt. Durch den Einzug des Rechners in den Mathematikunterricht wurden hierzu neue Möglichkeiten geschaffen: Multiple und dynamische Repräsentationen, die über Darstellungsgrenzen hinweg verschiedene Blickwinkel auf das gleiche Objekt verknüpfen, können heute mühelos erzeugt und interaktiv variiert werden. Mit Hilfe bestehender Theorien zu Repräsentationen und dem Argumentieren beantwortet die Arbeit die Frage, welchen Einfluss diese neuartigen Repräsentationen auf die Argumentationen von Schülerinnen und Schülern besitzen und leistet so einen Beitrag zur Diskussion über den Einsatz von digitalen Technologien im Mathematikunterricht.

Descartes on Polyhedra

A Study of the De Solidorum Elementis

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Author: P. J. Federico

Publisher: Springer Science & Business Media

ISBN: 146125759X

Category: Mathematics

Page: 145

View: 7067

The present essay stems from a history of polyhedra from 1750 to 1866 written several years ago (as part of a more general work, not published). So many contradictory statements regarding a Descartes manuscript and Euler, by various mathematicians and historians of mathematics, were encountered that it was decided to write a separate study of the relevant part of the Descartes manuscript on polyhedra. The contemplated short paper grew in size, as only a detailed treatment could be of any value. After it was completed it became evident that the entire manuscript should be treated and the work grew some more. The result presented here is, I hope, a complete, accurate, and fair treatment of the entire manuscript. While some views and conclusions are expressed, this is only done with the facts before the reader, who may draw his or her own conclusions. I would like to express my appreciation to Professors H. S. M. Coxeter, Branko Griinbaum, Morris Kline, and Dr. Heinz-Jiirgen Hess for reading the manuscript and for their encouragement and suggestions. I am especially indebted to Dr. Hess, of the Leibniz-Archiv, for his assistance in connection with the manuscript. I have been greatly helped in preparing the translation ofthe manuscript by the collaboration of a Latin scholar, Mr. Alfredo DeBarbieri. The aid of librarians is indispensable, and I am indebted to a number of them, in this country and abroad, for locating material and supplying copies.

A History of Mathematics

From Mesopotamia to Modernity

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Author: Luke Hodgkin

Publisher: OUP Oxford

ISBN: 9780191523830

Category: Mathematics

Page: 296

View: 9899

A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics (including Archimedes, Ptolemy, Qin Jiushao, al-Kashi, al-Khwarizmi, Galileo, Newton, Leibniz, Helmholtz, Hilbert, Alan Turing, and Andrew Wiles) and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises (with solutions) will stretch the more advanced reader.

Finite Projective Geometries

A Historical Approach with Emphasis on Finite Projective Planes

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Author: Lucille M. McKillop

Publisher: N.A

ISBN: N.A

Category: Geometry, Projective

Page: 315

View: 5276

Great Feuds in Mathematics

Ten of the Liveliest Disputes Ever

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Author: Hal Hellman

Publisher: Wiley

ISBN: N.A

Category: Mathematics

Page: 256

View: 3276

Praise for Hal Hellman Great Feuds in Mathematics "Those who think that mathematicians are cold, mechanical proving machines will do well to read Hellman's book on conflicts in mathematics. The main characters are as excitable and touchy as the next man. But Hellman's stories also show how scientific fights bring out sharper formulations and better arguments." -Professor Dirk van Dalen, Philosophy Department, Utrecht University Great Feuds in Technology "There's nothing like a good feud to grab your attention. And when it comes to describing the battle, Hal Hellman is a master." -New Scientist Great Feuds in Science "Unusual insight into the development of science . . . I was excited by this book and enthusiastically recommend it to general as well as scientific audiences." -American Scientist "Hellman has assembled a series of entertaining tales . . . many fine examples of heady invective without parallel in our time." -Nature Great Feuds in Medicine "This engaging book documents [the] reactions in ten of the most heated controversies and rivalries in medical history. . . . The disputes detailed are . . . fascinating. . . . It is delicious stuff here." -The New York Times "Stimulating." -Journal of the American Medical Association

Mathematics and the medieval ancestry of physics

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Author: George Molland

Publisher: Variorum Publishing

ISBN: 9780860784708

Category: Mathematics

Page: 336

View: 7870

The central theme of this volume lies in the medieval consciousness of mathematics, and the variety of strategies adopted to apply it in other areas, notably natural philosophy. In diachromic terms, Dr Molland considers ways in which ancient mathematics (particularly geometry) was assimilated in the Middle Ages, and how it was radically transformed in the 17th century, especially by Descartes. A pervasive concern is with ideas of scientific progress: the author argues that medieval commentatorial and disputational modes encouraged probing attitudes to existing knowledge, aimed at deepening individual understanding, rather than more aggressive endeavours to advance public knowledge characteristic of later periods. What brought about this change is the subject of several studies here; others form more specifically on individual scholars, in particular the important figure of Roger Bacon.

Journal of the Franklin Institute

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Meteorology

Page: N.A

View: 6413

Vols. 1-69 include more or less complete patent reports of the U. S. Patent Office for years 1825-1859. cf. Index to v. 1-120 of the Journal, p. [415]