2013/04/09 by Andrey M. Mishchenko, Mishchenko, Andrey M.
Materials Science · Mathematics · #2010: primary 52C26 #FOS: Mathematics #History and Overview (math.HO) #Mathematical Dynamics and Fractals #Mathematics and Applications #Quasicrystal Structures and Properties #math.HO #msc:00A08 #msc:52C26 #secondary 00A08
paper · pdf · doi:10.48550/arxiv.1304.2803
13 pages, 21 figures
arxiv created 2013/04/09 · openalex publication_date 2013/04/09 · arxiv updated 2013/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article is a gentle introduction to the mathematical area known as circle packing, the study of the kinds of patterns that can be formed by configurations of non-overlapping circles. The first half of the article is an exposition of the two most important facts about circle packings, (1) that essentially whatever pattern (i.e. combinatorics) we ask for, we may always arrange circles in that pattern, and (2) that under simple conditions on the pattern, there is an essentially unique arrangement of circles in that pattern. In the second half of the article, we consider related questions, but where we allow the circles to overlap. The article is written with the idea that no mathematical background should be required to read it.