Lines and Curves

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 Geometers 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.