Bo Söderberg
Lärare
Apollonian tiling, the Lorentz group, and regular trees
Författare
Summary, in English
The Apollonian tiling of the plane into circles is analyzed with respect to its group properties. The relevant group, which is noncompact and discrete, is found to be identical to the symmetry group of a particular geometric tree graph in hyperbolic three-space. A linear recursive method to compute the radii is obtained. Certain modifications of the problem are investigated, and relations to other problems, such as the universal scaling of circle maps, are pointed out.
Avdelning/ar
- Beräkningsbiologi och biologisk fysik - Har omorganiserats
Publiceringsår
1992
Språk
Engelska
Sidor
1859-1866
Publikation/Tidskrift/Serie
Physical Review A (Atomic, Molecular and Optical Physics)
Volym
46
Issue
4
Dokumenttyp
Artikel i tidskrift
Förlag
American Physical Society
Aktiv
Published
ISBN/ISSN/Övrigt
- ISSN: 1050-2947