Apollonian packings and hyperbolic geometry

Minoru Ishida, Sadayoshi Kojima

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We review the generalized apollonian packings by Bessis and Demko from 3-dimensional viewpoints and solve their conjectures on the discreteness of the groups they constructed. Moreover, we systematically generalize the construction of packings in terms of the Coxeter group theory, and propose a computational algorithm to draw the pictures efficiently based on the automatic group theory.

Original languageEnglish
Pages (from-to)265-283
Number of pages19
JournalGeometriae Dedicata
Volume43
Issue number3
DOIs
Publication statusPublished - 1992 Sep 1
Externally publishedYes

Fingerprint

Apollonian gasket
Lobachevskian geometry
Group Theory
Coxeter Group
Computational Algorithm
Packing
Generalise

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Apollonian packings and hyperbolic geometry. / Ishida, Minoru; Kojima, Sadayoshi.

In: Geometriae Dedicata, Vol. 43, No. 3, 01.09.1992, p. 265-283.

Research output: Contribution to journalArticle

Ishida, Minoru ; Kojima, Sadayoshi. / Apollonian packings and hyperbolic geometry. In: Geometriae Dedicata. 1992 ; Vol. 43, No. 3. pp. 265-283.
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