A Hilbert geometry is hyperbolic if and only if the perpendicular bisectors or the altitudes of any trigon form a pencil. We also prove some interesting characterizations of the ellipse
International audienceWe prove, in the context of Hilbert geometry, the equivalence between the exis...
We study oriented right-angled polygons in hyperbolic spaces of arbitrary dimensions, that is, fini...
National audienceThe use of massic points permits to define a branch of a hyperbola in the Euclidean...
If a Hilbert geometry satisfies a rather weak version of either Ceva’s or Menelaus’ theorem for ever...
In the dissertation, we present our research in the fields of projective metric geometries, in the c...
In general, when one refers to geometry, he or she is referring to Euclidean geometry. Euclidean geo...
In school, we learn that the interior angles of any triangle sum up to pi. However, there exist spac...
Abstract. The hyperbolic plane is an example of a geometry where the first four of Euclid’s Axioms h...
In the present dissertation we will introduce the historical development of the hyperbolic geometry....
EnWe point out that the axiomatic analysis of the statement The segments joining a point with the ve...
To contribute to the understanding of this paper, it is necessary to make some statement about notat...
In the Euclidean plane there are well-known constructions of points and tangents of e.g. an ellipse ...
Hilbert geometry is a metric geometry that extends the hyperbolic Cayley-Klein geometry. In this vid...
The main goal of this thesis is to introduce and develop the hyperboloid model of Hyperbolic Geometr...
We show that Euclidean Möbius planes can be axiomatized in terms of circles and circle-tangency, and...
International audienceWe prove, in the context of Hilbert geometry, the equivalence between the exis...
We study oriented right-angled polygons in hyperbolic spaces of arbitrary dimensions, that is, fini...
National audienceThe use of massic points permits to define a branch of a hyperbola in the Euclidean...
If a Hilbert geometry satisfies a rather weak version of either Ceva’s or Menelaus’ theorem for ever...
In the dissertation, we present our research in the fields of projective metric geometries, in the c...
In general, when one refers to geometry, he or she is referring to Euclidean geometry. Euclidean geo...
In school, we learn that the interior angles of any triangle sum up to pi. However, there exist spac...
Abstract. The hyperbolic plane is an example of a geometry where the first four of Euclid’s Axioms h...
In the present dissertation we will introduce the historical development of the hyperbolic geometry....
EnWe point out that the axiomatic analysis of the statement The segments joining a point with the ve...
To contribute to the understanding of this paper, it is necessary to make some statement about notat...
In the Euclidean plane there are well-known constructions of points and tangents of e.g. an ellipse ...
Hilbert geometry is a metric geometry that extends the hyperbolic Cayley-Klein geometry. In this vid...
The main goal of this thesis is to introduce and develop the hyperboloid model of Hyperbolic Geometr...
We show that Euclidean Möbius planes can be axiomatized in terms of circles and circle-tangency, and...
International audienceWe prove, in the context of Hilbert geometry, the equivalence between the exis...
We study oriented right-angled polygons in hyperbolic spaces of arbitrary dimensions, that is, fini...
National audienceThe use of massic points permits to define a branch of a hyperbola in the Euclidean...
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