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Original Articles

On the Last Geometric Statement of Jacobi

Pages 477-485 | Published online: 05 Apr 2012
 

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 R3 (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 −p (odd caustics). This is an extension of a statement usually attributed to Jacobi.

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