Torus Curves With Vanishing Curvature
Abstract
Let T be the standard torus of revolution in R3 with radii b and 1, 0<b<1. Let α be a (p,q) torus curve on T. We show that there are points of zero curvature on α for only one value of the variable radius of T, b=p2/(p2+q2). The curve α has non-vanishing curvature for all other values of b. Moreover, for this value of b, there are exactly q points of zero curvature on α.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.