info prev up next book cdrom email home

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 $k$ 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).


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.

© 1996-9 Eric W. Weisstein