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- Title
A Geometric Study of Circle Packings and Ideal Class Groups.
- Authors
Martin, Daniel E.
- Abstract
A family of fractal arrangements of circles is introduced for each imaginary quadratic field K. Collectively, these arrangements contain (up to an affine transformation) every set of circles in the extended complex plane with integral curvatures and Zariski dense symmetry group. When that set is a circle packing, we show how the ambient structure of our arrangement gives a geometric criterion for satisfying the asymptotic local–global principle. Connections to the class group of K are also explored. Among them is a geometric property that guarantees certain ideal classes are group generators.
- Subjects
QUADRATIC fields; CIRCLE; AFFINE transformations; GENERATORS of groups; SYMMETRY groups; BIANCHI groups
- Publication
Discrete & Computational Geometry, 2024, Vol 72, Issue 1, p181
- ISSN
0179-5376
- Publication type
Article
- DOI
10.1007/s00454-024-00638-w