Overview
- Novel reinterpretation of geometry in the context of motion, often viewing curves as trajectories of moving points
- This newly revised and expanded edition includes more than 200 theoretical and practical problems providing simple and elegant insight
- Interdisciplinary treatment is ideal for theoreticians, while accessible to undergraduates, advanced high school students, teachers, and puzzle enthusiasts alike
- Title already announced in Birkhäuser News 9-10/2002 / Titel wurde bereits in der Birkhäuser News Ausgabe 9-10/2002 angekündigt))
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Table of contents (9 chapters)
Keywords
About this book
Originally written in Russian and used in the Gelfand Correspondence School, "Lines and Curves" has since become a classic: the exposition maintains mathematical rigor while balancing creative storytelling and unusual examples of geometric properties. One of the key strengths of the text is its reinterpretation of geometry in the context of motion, whereby curves are realized as trajectories of moving points instead of as stationary configurations in the plane. This novel approach, rooted in physics and kinematics, yields surprisingly intuitive and straightforward proofs of many otherwise difficult results.
This newly revised and expanded edition includes more than 200 theoretical and practical problems in which formal geometry provides simple and elegant insight, including problems of maxima and minima and the construction of sets satisfying specific geometric constraints. Hence Lines and Curves is well positioned for companion use with software packages like The Geometer’s Sketchpad®, and it can serve as a guidebook for engineers. Its deeper, interdisciplinary treatment is ideal for more theoretical readers, and the development from first principles makes the book accessible to undergraduates, advanced high school students, teachers, and puzzle enthusiasts alike.
Reviews
"This book was originally published in Russian in 1978 and translated into English by A. Kundu for a 1980 edition. The present edition is based on that translation. It consists of brief expository sections followed by problems that are non-trivial and will be new to most American readers.... There is no book like this one, and it is well worth buying." —MAA Reviews
"If only some fo the ideas of this book would slip in teaching at school the pupils would not lament for boring mathematics. And if you [are looking] for a fasicinating, exciting, but by no means trivial approach to the beginnings of the theory of algebraic curves buy this book!" —Monashefte für Mathematik
"An engaging presentation, meant to attract young talent to the study of elementary geometry, of several topics in plane Euclidean geometry that share a certain `dynamic' quality: geometric loci, many of which are trajectories, being defined in terms of motions, minima and maxima, conic sections" —Zentralblatt Math
Authors and Affiliations
Bibliographic Information
Book Title: Lines and Curves
Book Subtitle: A Practical Geometry Handbook
Authors: Victor Gutenmacher, N. B. Vasilyev
DOI: https://doi.org/10.1007/978-1-4757-3809-4
Publisher: Birkhäuser Boston, MA
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 2004
Softcover ISBN: 978-0-8176-4161-0Published: 23 July 2004
eBook ISBN: 978-1-4757-3809-4Published: 14 March 2013
Edition Number: 1
Number of Pages: XVII, 156
Number of Illustrations: 90 b/w illustrations
Additional Information: Originally published by Mir Publishers, Moscow
Topics: Geometry, Theoretical and Applied Mechanics, Computer-Aided Engineering (CAD, CAE) and Design, Computer Graphics