Geometry Our Cultural Heritage
This book contains selected topics from the history of geometry, with "modern" proofs of some of the results, as well as a fully modern treatment of selected basic issues in geometry. It is geared towards the needs of future mathematics teachers. All too
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Audun Holme
Geometry Our Cultural Heritage Second Edition
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Audun Holme Department of Mathematics University of Bergen Johs. Brunsgt. 12 5008 Bergen Norway [email protected]
ISBN 978-3-642-14440-0 e-ISBN 978-3-642-14441-7 DOI 10.1007/978-3-642-14441-7 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010936506 c Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
This is a revised edition of the first printing which appeared in 2002. The book is based on lectures at the University of Bergen, Norway. Over the years these lectures have covered many different aspects and facets of the wonderful field of geometry. Consequently it has never been possible to give a full and final account of geometry as such, at an undergraduate level: A carefully considered selection has always been necessary. The present book constitutes the main central themes of these selections. One of the groups I am aiming at, is future teachers of mathematics. All too often the texts dealing with geometry which go into the syllabus for teacher-students present the material in ways which appear pedantic and formalistic, suppressing the very powerful and dynamic character of this old field, which at the same time so young. Geometry is a field of mathematical insight, research, history and source of artistic inspiration. And not least important, an integral part of our common cultural heritage. Another motivation is to provide an invitation to mathematics in general. It is an unfortunate fact that today, at a time when mathematics and knowledge of mathematics is more important than ever, the phenomena of math avoidance and math anxiety are very much present under different names all over the world. It is an important task to attempt seriously to heal these ills. Perhaps they are inflicted on students at an early age, through deficient or even harmful teaching practices. Thus the book also aims at an informed public, interested in making a new beginning in mathematics. And in doing so, learning more about this part of our cultural herita
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