The inversive plane and hyperbolic space

Coxeter, H. S. M.

doi:10.1007/bf03016050

Cited by 20 publications

(5 citation statements)

References 8 publications

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“…Similar ideas were expressed earlier. In the last section of [10], H. S. M. Coxeter writes: ... every projective statement in which one conic plays a special role can be translated into a statement about hyperbolic space.…”

Section: Introductionmentioning

confidence: 99%

Skewers

Tabachnikov

2016

Arnold Math J.

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Section: Introductionmentioning

confidence: 99%

Skewers

Tabachnikov

2016

Arnold Math J.

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“…The previous analysis of the effects of half-turns is still valid, with suitable modifications. For instance, when n = 10 there exist two a(5)'s, <*i(5) and a 2 (5) This discussion should be sufficient to indicate that many identities exist between products of a (m) 's.…”

Section: Infinite Chains Ofmentioning

confidence: 97%

Half-Turns and Infinite Chains of Clifford Configurations

Rigby¹

1982

Can. j. math.

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In a recent paper [7] Longuet-Higgins and Parry prove that, given a general Clifford configuration of degree 5 (abbreviated to CL5), C0 say, there exist points P and Q such that the inverses of P in the circles of C0 form the points of another CL5C1, whilst the inverses of Q in the circles of C1 are the points of C0; also the inverses of Q in the circles of C0 form the points of a CL5 C–1, whilst the inverses of P in the circles of C–1 are the points of C0. This leads to an infinite chain …, C–2, C–1, C0, C1, C2, … of CL5s, each connected to the next by means of the same two points P and Q, called the poles of the chain.

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“…In a nutshell, a skewer configuration theorem in 3dimensional hyperbolic space is a complexification of a configuration theorem in the hyperbolic plane. We follow the ideas of F. Morley [30,31], Coxeter [12], and V. Arnold [4]. Consider the hyperbolic space in the upper halfspace model.…”

Section: Skewersmentioning

confidence: 99%