Lines and Curves: A Practical Geometry Handbook - Softcover

Gutenmacher, Victor; Vasilyev, N.B.

Softcover

ISBN 10: 0817641610 ISBN 13: 9780817641610

Publisher: Birkhäuser, 2004

Synopsis

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.

About this title

From the Back Cover

"Lines and Curves" is a unique adventure in the world of geometry. Originally written in Russian and used in the Gelfand Correspondence School, this work has since become a classic: unlike standard textbooks that use the subject primarily to introduce axiomatic reasoning through formal geometric proofs, "Lines and Curves" maintains mathematical rigor, but also strikes a balance between creative storytelling and surprising examples of geometric properties. This newly revised and expanded edition includes more than 200 theoretical and practical problems in which formal geometry provides simple and elegant insight, and the book points the reader toward important areas of modern mathematics.

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 unusually intuitive and straightforward proofs of many otherwise difficult results. The geometrical properties of paths traced by moving points, the sets of points satisfying given geometric constraints, and questions of maxima and minima are all emphasized; therefore, "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. A wide audience will profit from this clear and diverse examination of the subject.

Edition details

• Publisher: Birkhäuser
• Publication date: 2004
• Language: English
• ISBN 10: 0817641610
• ISBN 13: 9780817641610
• Binding: Paperback
• Number of pages: 173