Lines and Curves A Practical Geometry Handbook [Paperback]

Broad appeal to undergraduate teachers, students, and engineers; Concise descriptions of properties of basic planar curves from different perspectives; useful handbook for software engineers; A special chapter--- Geometry on the Web ---will further enhance the usefulness of this book as an informal tutorial resource.; Good mathematical notation, descriptions of properties of lines and curves, and the illustration of geometric concepts facilitate the design of computer graphics tools and computer animation.; Video game designers, for example, will find a clear discussion and illustration of hard-to-understand trajectory design concepts.; Good supplementary text for geometry courses at the undergraduate and advanced high school levels

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 minimalc-