A theorem on circle configurations
arXiv:0706.0372
Abstract
A formula for the radii and positions of four circles in the plane for an arbitrary linearly independent circle configuration is found. Among special cases is the recent extended Descartes Theorem on the Descartes configuration and an analytic solution to the Apollonian problem. The general theorem for n-spheres is also considered.
16 pages, 13 figures
Cited by in corpus (13)
- On a Diophantine equation that generates all integral Apollonian Gaskets
- A note on unbounded Apollonian disk packings
- Visualising the arithmetic of imaginary quadratic fields
- Proof of Descartes circle formula and its generalization clarified
- Spinors and Descartes configurations of disks
- Apollonian depth, spinors, and the super-Dedekind tessellation
- Spinors, lattices, and classification of integral Apollonian disk packings
- Apollonian coronas and a new Zeta function
- On the Dedekind tessellation
- Domains of Convergence for Polyhedral Packings
- Integral spinors, Apollonian disk packings, and Descartes groups
- Tessellations and Descartes disk configurations
- Fibonacci numbers and Ford circles