Incidence theorems in spaces of constant curvature
@article{Masaltsev1994IncidenceTI,
title={Incidence theorems in spaces of constant curvature},
author={L. A. Masal’tsev},
journal={Journal of Mathematical Sciences},
year={1994},
volume={72},
pages={3201-3206}
}Certain analogs of the classic theorems of Menelaus and Ceva are considered for a hyperbolic surface, a sphere, and for three-dimensional hyperbolic and spherical spaces.
10 Citations
Ceva’s and Menelaus’ theorems in projective-metric spaces
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In this study, we give isogonal conjugates from major contributions of the modern synthetic geometry of the hyperbolic triangle in Poincaré upper half plane model of hyperbolic geometry.
Ceva, Menelaus, and Selftransversality
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Another proof of the Steiner—Routh theorem for tetrahedra is given, where methods of elementary geometry are combined with the inclusion—exclusion principle, and this approach is generalized to (n — 1)-dimensional simplices.
On curves with the Poritsky property
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Reflection in planar billiard acts on oriented lines. For a given closed convex planar curve $$\gamma $$ γ , the string construction yields a one-parameter family $$\Gamma _p$$ Γ p of nested billiard…
Covering of a Reduced Spherical Body by a Disk
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We prove the following theorems: (1) every spherical convex body W of constant width ΔW≥π2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}…
On curves with the Poritsky property
- Materials ScienceJournal of Fixed Point Theory and Applications
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Reflection in planar billiard acts on oriented lines. For a given closed convex planar curve γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}…
Covering of a Reduced Spherical Body by a Disk
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- 2021
We prove the following theorems: (1) every spherical convex body W of constant width Δ W ≥ π 2 $$ \varDelta (W)\ge \frac{\uppi}{2} $$ can be covered by a disk of radius Δ W + arcsin 2 3 3 cos Δ W 2 −…
Determining modes and nodes of the rotating Navier-Stokes equations
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It is proved under reasonable hypotheses that the number of determining modes is bounded by $c\mathcal{G}^{1/2}+ \epsilon^{1-2}M$, where $1/\ep silon$ is the rotation rate and $M$ depends on up to third derivatives of the forcing.
ISOGONAL CONJUGATES IN POINCARE UPPER HALF PLANE
- Mathematics
- 2011
In this study, we give isogonal conjugates from major contributions of the modern synthetic geometry of the triangle in hyperbolic plane. Key Words: Hyperbolic Ceva theorem and Hyperolic sines theorem