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On Jacobi's remarkable curve theorem

✍ Scribed by John McCleary

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
439 KB
Volume
21
Category
Article
ISSN
0315-0860

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✦ Synopsis

FOR DIRK STRUIK ON HIS |00TH BIRTHDAY

One of the prettiest results in the global theory of curves is a theorem of Jacobi (1842):

The spherical image of the normal directions along a closed differentiable curve in space divides the unit sphere into regions of equal area. The statement of this theorem is an afterthought to a paper in which Jacobi responds to the published correction by Thomas Clausen (1842) of an earlier paper, Jacobi (1836). In this note the context for this theorem and its proof are presented as well as a discussion of the 'error' corrected by Clausen.

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