2021/01/11 by Yury Kochetkov, Kochetkov, Yury
Computer Science · Mathematics · #Cellular Automata and Applications #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Metric Geometry (math.MG) #math.MG
paper · pdf · doi:10.48550/arxiv.2101.03734
8 pages, 8 figures
arxiv created 2021/01/11 · openalex publication_date 2021/01/11 · arxiv updated 2021/01/12 · openalex created_date 2021/01/18 · openalex updated_date 2026/07/28
Let M be the space of triangles, defined up to shifts, rotations and dilations. We define two maps f:M→ M and g:M→ M. The map f corresponds to a triangle of perimeter π the triangle with angles numerically equal to edges of the initial triangle. The map g corresponds to a triangle of perimeter 2π the triangle with exterior angles numerically equal to edges of the initial triangle. For p∈ M the sequence \p,f(p),f(f(p)),…\ converges to the equilateral triangle and the sequence \p,g(p),g(g(p)),…\ converges to the "degenerate triangle" with angles (0,0,π). In Supplement an analogous problem about inscribed-circumscribed quadrangles is discussed.