Clélies
Sign in to saveAlso known as Clelies
thumb|upright=1.2|Clelia curve for c=1/4 with an orientation (arrows) (At the coordinate axes the curve runs upwards, see the corresponding floorplan below, too) thumb|upright=1.4|Clelia curves: floor plans of examples, arcs on the lower half of the sphere are dotted. The last four curves (spherical spirals) start at the south pole and end at the northpole. The upper four curves are due to the choice of parameter c periodic (see: Rose (mathematics)|rose).
~3 min read
Article
4 sectionsContents
- Parametric representation
- Examples
- References
- External links
thumb|upright=1.2|Clelia curve for c=1/4 with an orientation (arrows) (At the coordinate axes the curve runs upwards, see the corresponding floorplan below, too) thumb|upright=1.4|Clelia curves: floor plans of examples, arcs on the lower half of the sphere are dotted. The last four curves (spherical spirals) start at the south pole and end at the northpole. The upper four curves are due to the choice of parameter c periodic (see: Rose (mathematics)|rose).
In mathematics, a Clélie or Clelia curve is a curve on a sphere with the property: If the surface of a sphere is described as usual by the longitude (angle \varphi) and the colatitude (angle \theta) then \varphi=c\;\theta, \quad c>0.