Namespaces
Variants
Actions

Joachimsthal surface

From Encyclopedia of Mathematics
Revision as of 17:26, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

The surface formed by the orthogonal trajectories of a one-parameter family of spheres with centres on a straight line. If the -axis is taken for this straight line, if the -coordinates of the centres of the spheres are denoted by , and if the radius of the sphere is denoted by , then the position vector of the Joachimsthal surface is:

where

One of the families of curvature lines of the Joachimsthal surface is located in the planes of a pencil. The surface was studied by F. Joachimsthal [1].

References

[1] F. Joachimsthal, "Demonstratio theorematum ad superficies curvas spectantium" J. Reine Angew. Math. , 30 (1846) pp. 347–350


Comments

References

[a1] G. Darboux, "Leçons sur la théorie générale des surfaces et ses applications géométriques du calcul infinitésimal" , 1 , Gauthier-Villars (1887) pp. 1–18
How to Cite This Entry:
Joachimsthal surface. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Joachimsthal_surface&oldid=33305
This article was adapted from an original article by I.Kh. Sabitov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article