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2003 On the Last Geometric Statement of Jacobi
R. Sinclair
Experiment. Math. 12(4): 477-486 (2003).

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.

Citation

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R. Sinclair. "On the Last Geometric Statement of Jacobi." Experiment. Math. 12 (4) 477 - 486, 2003.

Information

Published: 2003
First available in Project Euclid: 18 June 2004

zbMATH: 1073.53007
MathSciNet: MR2043997

Subjects:
Primary: 53C20
Secondary: 53-04

Keywords: Caustic , conjugate locus , ellipsoid

Rights: Copyright © 2003 A K Peters, Ltd.

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Vol.12 • No. 4 • 2003
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