Random triangles on flat tori
نویسندگان
چکیده
Inspired by classical puzzles in geometry that ask about probabilities of geometric phenomena, we give an explicit formula for the probability a random triangle on flat torus is homotopically trivial. Our main tool this computation involves reducing problem to new invariant measurable sets plane unchanged under area-preserving affine transformations. result show minimized at all rectangular tori and maximized regular hexagonal torus.
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2022
ISSN: ['0035-7596', '1945-3795']
DOI: https://doi.org/10.1216/rmj.2022.52.1345