Mathematical Field Notes

Cone eversion

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Last year, around the time Chris Wendl was running the h-principle learning seminar at UCL, I set my second years an exercise from Eliashberg-Mishachev as a difficult challenge problem: to find an explicit cone eversion. In other words, find a path in the space of functions on \{(r,\theta)\in\mathbf{R}^2\ :\ r\in[1,2]\} connecting r to 2-r such that none of the intermediate functions has a critical point. One of these students, Tom Steeples, got hooked on the problem, almost solved it, and afterwards used Mathematica to produce some beautiful computer animations of a solution given by Tabachnikov in American Mathematical Monthly (1995) Vol 102, Issue 1, pp 52–56. Here, below the fold because it’s quite a large file, is one of his images. Reproduced with Tom’s kind permission (the copyright is his).

Cone eversion

A cone everting, (C) Tom Steeples 2014.


Written by Jonny Evans

October 12, 2014 at 2:02 pm

Posted in Uncategorized

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