Seiffert's spiral
   HOME

TheInfoList



OR:

Seiffert's spherical spiral is a curve on a sphere made by moving on the sphere with constant speed and angular velocity with respect to a fixed diameter. If the selected diameter is the line from the north pole to the south pole, then the requirement of constant angular velocity means that the longitude of the moving point changes at a constant rate. The cylindrical coordinates of the varying point on this curve are given by the Jacobian elliptic functions.


Formulation


Symbols


Representation via equations

The Seiffert's spherical spiral can be expressed as r = \operatorname(s, k),\, \theta = k \cdot s \text z = \operatorname(s, k) or expressed as
Jacobi theta functions In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field ...
r = \frac,\, \theta = \frac \cdot s \text z = \frac.


See also

* Rhumb line


References

* *


External links

* Spirals Spherical curves {{geometry-stub