2 papers
math.DG2025
Bicycle tracks with hyperbolic monodromy -- results and conjectures
G. Bor, L. Hernández-Lamoneda, S. Tabachnikov
We find new necessary and sufficient conditions for the bicycling monodromy of a closed plane curve to be hyperbolic. Our main tool is the ``hyperbolic development" interpretation…
math.DG2024
A 4-point theorem: still another variation on an old theme
Serge Tabachnikov
An old theorem, due to Graustein, asserts that the average curvature of a plane oval is attained at least at four points. We present a proof by way of wave propagation and extend t…