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About: Last geometric statement of Jacobi     Goto   Sponge   NotDistinct   Permalink

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In differential geometry the last geometric statement of Jacobi is a conjecture named after Carl Gustav Jacob Jacobi. According to this conjecture: Every caustic from any point on an ellipsoid other than umbilical points has exactly four cusps. While numerical experiments had indicated the statement is true, it wasn’t until 2004 that it was proven rigorously by Itoh and Kiyohara. It has since been extended to a wider class of surfaces beyond the ellipsoid.