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- W1670588671 abstract "The Tait-Kneser theorem, first demonstrated by Peter G. Tait in 1896, states that the osculating circles along a plane curve with monotone non-vanishing curvature are pairwise disjoint and nested. This note contains a proof of this theorem using the Lorentzian geometry of the space of circles. We show how a similar proof applies to two variations on the theorem, concerning the osculating Hooke and Kepler conics along a plane curve. We also prove a version of the 4-vertex theorem for Kepler conics." @default.
- W1670588671 created "2016-06-24" @default.
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- W1670588671 date "2021-04-05" @default.
- W1670588671 modified "2023-10-02" @default.
- W1670588671 title "Variations on the Tait-Kneser theorem" @default.
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- W1670588671 doi "https://doi.org/10.48550/arxiv.2104.02170" @default.
- W1670588671 hasPublicationYear "2021" @default.
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