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On the last geometric statement of Jacobi. (English) Zbl 1073.53007

The last geometric statement of Jacobi concerns the structure of the conjugate locus of a point in an ellipsoid. The claim is that this always has four cusps. A more general version would include the statement that the cut locus of a point is an arc on the curvature line through the antipodal point. The present paper contains numerical experiments which support these statements. A number of nice figures are given which indicate the four cusps. For a description of a computer tool called Thaw see J. Itoh and the author in [Exp. Math. 13, 309–325 (2004)]. Both statements were later proven without a computer by J. Itoh and K. Kiyohara in [Manuscr. Math. 114, No. 2, 247–264 (2004; Zbl 1076.53042)].

MSC:

53A05 Surfaces in Euclidean and related spaces
53-04 Software, source code, etc. for problems pertaining to differential geometry

Citations:

Zbl 1076.53042

Software:

Loki; Thaw
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