"Lines and Curves" is a unique adventure in the world of geometry. Originally written in Russian and used in the Gelfand Correspondence School, the book has since become a classic: unlike standard textbooks that use the subject primarily to introduce axiomatic reasoning as illustrated by formal geometric proofs, "Lines and Curves" maintains solid mathematical rigor, but also strikes a balance between whimsical artistry, 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.
The text focuses on the geometrical properties of paths traced by moving points, the sets of points satisfying given geometric constraints, and questions of maxima and minima; it is, therefore, well positioned for companion use with software packages like Geometry Sketchpad, and can serve as a guidebook for engineers. Its deeper, interdisciplinary treatment of geometry also makes it ideal for those interested in the subject purely for its beauty, and the development of "Lines and Curves" from first principles makes it accessible to high school students, teachers, and puzzle enthusiasts alike. A wide audience will profit from its careful treatment of geometry and its synthesis of many branches of mathematics.
Based on an English translation of the Russian edition by A. Kundu, Saha Istitute of Nuclear Physics, Calcutta, India.
