A geometric interpretation of Ungar's addition and of gyration in the hyperbolic plane

We present a geometric interpretation of the operation a ⊕ b and the gyration on the unit-disc as defined by A.A. Ungar. Using this geometric interpretation we show that the two known generalizations to the n-dimensional unit ball are identical. The interpretation in the plane leads us to the notion...

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Bibliographic Details
Published inTopology and its applications Vol. 152; no. 3; pp. 226 - 242
Main Author Vermeer, J.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 14.07.2005
Subjects
Gyration
Hyperbolic plane
Ungar's addition
secondary
Hyperbolic plane
Ungar's addition
Gyration
primary
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Summary:We present a geometric interpretation of the operation a ⊕ b and the gyration on the unit-disc as defined by A.A. Ungar. Using this geometric interpretation we show that the two known generalizations to the n-dimensional unit ball are identical. The interpretation in the plane leads us to the notion of outer-median of a triangle and we discuss some possible properties of this median.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2004.10.012