Year: 2025
Type: article
Abstract: A topological disc is called n -self-affine if it has a dissection into n affine images of itself. It is called n -gc-self-affine if the dissection is obtained by successive glass-cuts, which are cuts along segments splitting one disc into two. For every $$n \ge 2$$ n ≥ 2 , we characterize all n -gc-self-affine discs. All such discs turn out to be either triangles or convex quadrangles. All triangles and trapezoids are n -gc-self-affine for every n . Non-trapezoidal quadrangles are not n -gc-self-affine for even n . They are n -gc-self-affine for every odd $$n \ge 7$$ n ≥ 7 , and they are n -gc-self-affine for $$n=5$$ n = 5 if they aren’t affine kites. Only four one-parameter families of quadrangles turn out to be 3-gc-self-affine. In addition, we show that every convex quadrangle is n -self-affine for all $$n \ge 5.$$ n ≥ 5 .
Author: Christian Richter
Institution: Friedrich Schiller University Jena
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4415225379