Apollonian packings and hyperbolic geometry

Minoru Ishida; Sadayoshi Kojima

doi:10.1007/BF00151517

Apollonian packings and hyperbolic geometry

Minoru Ishida, Sadayoshi Kojima

Research output: Contribution to journal › Article

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 language	English
Pages (from-to)	265-283
Number of pages	19
Journal	Geometriae Dedicata
Volume	43
Issue number	3
DOIs	https://doi.org/10.1007/BF00151517
Publication status	Published - 1992 Sep 1
Externally published	Yes

Fingerprint

Apollonian gasket

Lobachevskian geometry

Group Theory

Coxeter Group

Computational Algorithm

Packing

Generalise

ASJC Scopus subject areas

Geometry and Topology

Cite this

Ishida, M., & Kojima, S. (1992). Apollonian packings and hyperbolic geometry. Geometriae Dedicata, 43(3), 265-283. https://doi.org/10.1007/BF00151517

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 journal › Article

Ishida, M & Kojima, S 1992, 'Apollonian packings and hyperbolic geometry', Geometriae Dedicata, vol. 43, no. 3, pp. 265-283. https://doi.org/10.1007/BF00151517

Ishida M, Kojima S. Apollonian packings and hyperbolic geometry. Geometriae Dedicata. 1992 Sep 1;43(3):265-283. https://doi.org/10.1007/BF00151517

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

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Access to Document

10.1007/BF00151517