On the Last Geometric Statement of Jacobi
Sinclair, R.
Experiment. Math., Tome 12 (2003) no. 1, p. 477-486 / Harvested from Project Euclid
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Based upon numerical experimentation, we claim that all caustics from any nonumbilical (nonpolar for ellipsoids of revolution) point p on any ellipsoid embedded in {\small $\mathbb{R}^3$} (except the 2-sphere) have exactly four cusps, all of which are on lines of curvature (meridians and parallels for ellipsoids of revolution) intersecting either p (even caustics) or {\small $-p$} (odd caustics). This is an extension of a statement usually attributed to Jacobi.
Publié le : 2003-05-14
Classification:  Conjugate locus,  caustic,  ellipsoid,  53C20,  53-04 
@article{1087568023,
     author = {Sinclair, R.},
     title = {On the Last Geometric Statement of Jacobi},
     journal = {Experiment. Math.},
     volume = {12},
     number = {1},
     year = {2003},
     pages = { 477-486},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1087568023}
}

Sinclair, R. On the Last Geometric Statement of Jacobi. Experiment. Math., Tome 12 (2003) no. 1, pp.  477-486. http://gdmltest.u-ga.fr/item/1087568023/