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July 29 – 210

Mathematica 10.1 The “last geometric statement of Jacobi” says that the conjugate locus of a non-umbilic point on the triaxial ellipsoid has four cusps – which was later proved by Itoh and Kiyohara. Here is an artistic interpretation of a locus of conjugate points along a “spray” of unit speed geodesics emanating from a “base point” on the ellipsoid. From an original script by Thomas Waters.