%0 Journal Article
%T An Explicit Formula for the Spherical Curves with Constant Torsion
%A Demetre Kazaras
%A Ivan Sterling
%J Mathematics
%D 2013
%I arXiv
%X The purpose of this article is to give an explicit formula for all curves of constant torsion $\tau$ in the unit two-sphere $S^2(1)$. These curves and their basic properties have been known since the 1890's, and some of these properties are discussed in the Appendix. Some example curves, computed with a standard ODE package, with $\tau=.1,.5,1,2$ are shown in Figure \ref{peter}. Though their existence and some of their general properties were known, our explicit formulas for them, in terms of hypergeometric functions, are new.
%U http://arxiv.org/abs/1312.0140v1