## Experimental Mathematics

### On the Last Geometric Statement of Jacobi

R. Sinclair

#### Abstract

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.

#### Article information

Source
Experiment. Math., Volume 12, Number 4 (2003), 477-486.

Dates
First available in Project Euclid: 18 June 2004

https://projecteuclid.org/euclid.em/1087568023

Mathematical Reviews number (MathSciNet)
MR2043997

Zentralblatt MATH identifier
1073.53007

Keywords
Conjugate locus caustic ellipsoid

#### Citation

Sinclair, R. On the Last Geometric Statement of Jacobi. Experiment. Math. 12 (2003), no. 4, 477--486. https://projecteuclid.org/euclid.em/1087568023