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Constructions In Hyperbolic Geometry
Canadian Journal of Mathematics, 1956Introduction. In hyperbolic geometry we have three compasses, namely an ordinary compass for drawing ordinary circles with a given centre and a given radius, a hypercompass for drawing hypercycles with a given axis and a given radius, and a horocompass for drawing horocycles with a given diameter and passing through a given point.
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Correction to “Axiomatizations of Hyperbolic Geometry”
Synthese, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Martingales in Hyperbolic Geometry
2014The famous De Moivre-Laplace theorem states the convergence toward a gaussian law of \(\sum\limits_{j=0}^{n-1}Y _{j}/\sqrt{n}\) when the Y i are independent, centered, identically distributed random variables in L 2. This result is usually named Central Limit Theorem (CLT). The convergence still holds in some non independent cases (Markov chains, α- or
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1992
Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics. In this book, the rich geometry of the hyperbolic plane is studied in detail, leading to the focal point of the book, Poincare's polygon ...
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Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics. In this book, the rich geometry of the hyperbolic plane is studied in detail, leading to the focal point of the book, Poincare's polygon ...
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Ptolemy’s Theorem in the Relativistic Model of Analytic Hyperbolic Geometry
Symmetry, 2023Abraham Ungar
exaly
The Hyperbolic Ptolemy’s Theorem in the Poincaré Ball Model of Analytic Hyperbolic Geometry
Symmetry, 2023Abraham Ungar
exaly
Information geometry of hyperbolic-valued Boltzmann machines
Neurocomputing, 2021Masaki Kobayashi
exaly