REVIEW 1 cited by
On Menelaus' and Ceva's theorems in Nil geometry
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
In this paper we deal with $\NIL$ geometry, which is one of the homogeneous Thurston 3-geometries. We define the "surface of a geodesic triangle" using generalized Apollonius surfaces. Moreover, we show that the "lines" on the surface of a geodesic triangle can be defined by the famous Menelaus' condition and prove that Ceva's theorem for geodesic triangles is true in $\NIL$ space. In our work we will use the projective model of $\NIL$ geometry described by E. Moln\'ar in \cite{M97}.
Forward citations
Cited by 1 Pith paper
-
Menelaus' and Ceva's theorems for translation triangles in Thurston geometries
Menelaus' and Ceva's theorems are formulated and proved for translation triangles in Nil, Sol, and ~SL2R spaces using geometry-specific simple ratios.
Discussion (0). Continue with ORCID to comment.