2022/05/23 by Miklos Laczkovich, Laczkovich, Miklos
Mathematics · #52A10 #52C20 #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:52A10 #msc:52C20
paper · pdf · doi:10.48550/arxiv.2205.11068
arxiv created 2022/05/23 · arxiv updated 2022/05/24
A polygon P is called a reptile, if it can be decomposed into k≥ 2 nonoverlapping and congruent polygons similar to P. We prove that if a cyclic quadrilateral is a reptile, then it is a trapezoid. Comparing with results of U. Betke and I. Osburg we find that every convex reptile is a triangle or a trapezoid.