# Lines and Curves

## A Practical Geometry Handbook

• Victor Gutenmacher
• N. B. Vasilyev
Textbook

1. Front Matter
Pages i-xvii
2. Victor Gutenmacher, N. B. Vasilyev
Pages 1-5
3. Victor Gutenmacher, N. B. Vasilyev
Pages 7-17
4. Victor Gutenmacher, N. B. Vasilyev
Pages 19-34
5. Victor Gutenmacher, N. B. Vasilyev
Pages 35-46
6. Victor Gutenmacher, N. B. Vasilyev
Pages 47-54
7. Victor Gutenmacher, N. B. Vasilyev
Pages 55-66
8. Victor Gutenmacher, N. B. Vasilyev
Pages 67-88
9. Victor Gutenmacher, N. B. Vasilyev
Pages 89-109
10. Victor Gutenmacher, N. B. Vasilyev
Pages 111-126
11. Back Matter
Pages 127-156

### Introduction

"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.

### Keywords

Area CAD programming animation computer animation computer graphics construction geometry kinematics ksa sketch

#### Authors and affiliations

• Victor Gutenmacher
• 1
• N. B. Vasilyev
1. 1.BrooklineUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4757-3809-4
• Copyright Information Birkhäuser Boston 2004
• Publisher Name Birkhäuser, Boston, MA
• eBook Packages
• Print ISBN 978-0-8176-4161-0
• Online ISBN 978-1-4757-3809-4
• Buy this book on publisher's site