  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.
