2001/01/01 by C. G. Gibson · 2 citations
Engineering · Mathematics · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Arc (geometry) #Arc length #Calculus (dental) #Classical mechanics #Computer graphics (images) #Computer science #Curvature #Cusp (singularity) #Differentiable function #Differential equation #Differential geometry #Differential geometry of curves #Euclidean geometry #Geometry #Kinematics #Mathematical analysis #Mathematics #Mathematics and Applications #Ordinary differential equation #Physics #Planar #Plane (geometry) #Plane curve #Pure mathematics #Robotic Mechanisms and Dynamics #Section (typography) #Uniqueness
paper · doi:10.1017/cbo9781139173377
openalex publication_date 2001/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15
This genuine 2001 introduction to the differential geometry of plane curves is designed as a first text for undergraduates in mathematics, or postgraduates and researchers in the engineering and physical sciences. The book assumes only foundational year mathematics: it is well illustrated, and contains several hundred worked examples and exercises, making it suitable for adoption as a course text. The basic concepts are illustrated by named curves, of historical and scientific significance, leading to the central idea of curvature. The singular viewpoint is represented by a study of contact with lines and circles, illuminating the ideas of cusp, inflexion and vertex. There are two major physical applications. Caustics are discussed via the central concepts of evolute and orthotomic. The final chapters introduce the core material of classical kinematics, developing the geometry of trajectories via the ideas of roulettes and centrodes, and culminating in the inflexion circle and cubic of stationary curvature