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Professor: Gil Bor, CIMAT, Guanajuato, gil@cimat.mx
Schedule: Tuesday and Thursday, 13:30-15:00, Mar 19 -- Apr 4, 2024 (6 sessions total, can be extended upon demand).
Place: 1st session (March 19): room Johnson 1R3; afterwards: room Cavaillès 1R2.
Directed to: Master students (mainly), but all interested students+faculty are welcome.
Description: this is a topics course covering classical aspects of the differential geometry of plane curves, as well as some contemporary variations and developments (as time permits). The emphasis is less on definitions and more on interesting examples and nice results: the 4 vertex theorem, the Tate-Kneser nesting theorem, evolutes and involutes, bicycle trajectories, the classical curves (cycloid, catenary, tractrix, elastica,...). The pre-requisites are a standard undergraduate vector calculus course, curiosity and mind open to new ideas.
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| The figure illustrates the Tait-Kneser theorem, on the nesting of the osculating circles along a plane curve with monotone curvature (in this case an Archemidean spiral). Taken from my article Variations on the Tait-Kneser theorem (with C. Jackman and S. Tabachnikov), Math. Intelligencer 43 (2021).
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