Seifert's Spherical Spiral

Is given by the Cylindrical Coordinates parametric equation

$\displaystyle r$	$\textstyle =$	$\displaystyle \mathop{\rm sn}\nolimits (s)$
$\displaystyle \theta$	$\textstyle =$	$\displaystyle ks$
$\displaystyle z$	$\textstyle =$	$\displaystyle \mathop{\rm cn}\nolimits (s),$

where

is a Positive constant and $\mathop{\rm sn}\nolimits (s)$ and $\mathop{\rm cn}\nolimits (s)$ are Jacobi Elliptic Functions (Whittaker and Watson 1990, pp. 527-528).

References

Bowman, F. Introduction to Elliptic Functions, with Applications. New York: Dover, p. 34, 1961.

Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, 1990.