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
