This paper is meant to be a guide to various derived curves. It focuses on five primary types of derived curves, including the evolute, involute, parallel curve, pedal curve and envelope. The topics of this paper rely on basic calculus skills and concepts, including differentiation, tangent and normal vectors, arc length and curvature. There is a specific section or chapter devoted to each type of derived curve and each one includes the basic definition of the curve and how it is constructed, its parametric equations and numerous examples using a variety of curves. The examples are usually accompanied by an explanation of how the new curve was attained and include pictures of the original curve and the derived curve or curves graphed together. Theorems and proofs have been included where they are necessary in order to make a concept clearer to the reader, or if they somehow add to the topic at hand in some way, highlighting an interesting result or connection between different curves.
Mathematics; Computer Science
Stroud, Elizabeth, "Exploration of Curves" (2008). Senior Independent Study Theses. Paper 904.
Bachelor of Arts
Senior Independent Study Thesis
© Copyright 2008 Elizabeth Stroud