## Experimental Mathematics

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

### On the Last Geometric Statement of Jacobi

#### 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

**Permanent link to this document**

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

**Mathematical Reviews number (MathSciNet)**

MR2043997

**Zentralblatt MATH identifier**

1073.53007

**Subjects**

Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]

Secondary: 53-04: Explicit machine computation and programs (not the theory of computation or programming)

**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.