# 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

- MathematicsJournal of Geometry
- 2019

AbstractWe prove that Ceva’s and Menelaus’ theorems are valid in a projective-metric space if and only if the space is any of the elliptic geometry, the hyperbolic geometry, or the Minkowski…

### Isogonal Conjugates in Poincaré Upper Half Plane

- Mathematics
- 2011

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

- Mathematics
- 1997

The purpose of this paper is to state and prove a theorem (the CMS Theorem) which generalizes the familiar Ceva's Theorem and Menelaus' Theorem of elementary Euclidean geometry. The theorem concernsn…

### On the Steiner–Routh Theorem for Simplices

- MathematicsAm. Math. Mon.
- 2017

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

- MathematicsJournal of Fixed Point Theory and Applications
- 2022

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

- MathematicsUkrainian Mathematical Journal
- 2021

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
- 2022

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

- Mathematics
- 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

- Computer Science
- 2019

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