Total Normalcy of Knots

Abstract

In this paper we consider first order infinitesimal bending of curves and knots. The total normalcy of the knot during the first order infinitesimal bending is discussed and expressions for the first variation of the total normalcy are given. Some examples aimed to illustrate infinitesimal bending of knots are shown using figures. Colors are used to illustrate normalcy values at dierent points of bent knots and the total normalcy is numerically calculated.