Hyperbolic Triangle Centers The Special Relativistic Approach
After A. Ungar had introduced vector algebra and Cartesian coordinates into hyperbolic geometry in his earlier books, along with novel applications in Einstein’s special theory of relativity, the purpose of his new book is to introduce hyperbolic barycent
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Fundamental Theories of Physics
An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application
Series Editors: PHILIPPE BLANCHARD, Universität Bielefeld, Bielefeld, Germany PAUL BUSCH, University of York, Heslington, York, UK BOB COECKE, Oxford University Computing Laboratory, Oxford, UK DETLEF DUERR, Mathematisches Institut, Munich, Germany ROMAN FRIGG, London School of Economics and Political Science, London, UK CHRISTOPHER A. FUCHS, Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada GIANCARLO GHIRARDI, University of Trieste, Trieste, Italy DOMENICO GIULINI, University of Hannover, Hannover, Germany GREGG JAEGER, Boston University CGS, Boston, USA CLAUS KIEFER, University of Cologne, Cologne, Germany KLAAS LANDSMANN, Radboud Universiteit Nijmegen, Nijmegen, The Netherlands CHRISTIAN MAES, K.U. Leuven, Leuven, Belgium HERMANN NICOLAI, Max-Planck-Institut für Gravitationsphysik, Golm, Germany VESSELIN PETKOV, Concordia University, Montreal, Canada ALWYN VAN DER MERWE, University of Denver, Denver, USA RAINER VERCH, Universität Leipzig, Leipzig, Germany REINHARD WERNER, Leibniz University, Hannover, Germany CHRISTIAN WÜTHRICH, University of California, San Diego, La Jolla, USA
Volume 166 For other titles published in this series, go to http://www.springer.com/series/6001
A.A. Ungar
Hyperbolic Triangle Centers The Special Relativistic Approach
Prof. A.A. Ungar Dept. Mathematics 2750 North Dakota State University 58108-6050 Fargo, ND USA [email protected]
ISBN 978-90-481-8636-5 e-ISBN 978-90-481-8637-2 DOI 10.1007/978-90-481-8637-2 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2010930171 © Springer Science+Business Media B.V. 2010 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Cover design: eStudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To my Daughters and Sons Tamar, Ziva, Ilan and Ofer and to my Grandchildren
Preface
The seeds of this book were planted in 1988 [55], when the author discovered that the seemingly structureless Einstein addition of relativistically admissible velocities possesses rich nonassociative algebraic structures that became known as a gyrocommutative gyrogroup and a gyrovector space. Einstein gyrovector spaces turn out to form the algebraic setting for the Cartesian–Beltrami–Klein ball model of the hyperbolic geometry of János Bolyai and Nikolai Ivanovich Lobachevsky, just as vector spaces form the algebraic setting for the standard Cartesian model of Euclidean geometry. This book presents the novel approach to triangle centers in hyperbol
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