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. 
View on Springer
9 Citations
Background Citations
1
Methods Citations
2

9 Citations

Ceva’s and Menelaus’ theorems in projective-metric spaces

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

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

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…

Covering a reduced spherical body by a disk

  • M. Musielak
  • Mathematics
    Ukrains’kyi Matematychnyi Zhurnal
  • 2020
UDC 514 In this paper, the following theorems are proved: (1) every spherical convex body of constant width may be covered by a disk of radius (2) every reduced spherical convex body of thickness may…

On the Steiner–Routh Theorem for Simplices

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.

Determining modes and nodes of the rotating Navier-Stokes equations

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.

On curves with the Poritsky property

  • A. Glutsyuk
  • Mathematics
    Journal 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

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 −…

ISOGONAL CONJUGATES IN POINCARE UPPER HALF PLANE

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