Ponceletsche Dreieckscharen.
Quadratische Identitäten bei Polygonen.
Reconstructing Plane Sets from Projections.
Relations on lines as primitive notions for Euclidean geometry
Routh’s, Menelaus’ and Generalized Ceva’s Theorems
The goal of this article is to formalize Ceva’s theorem that is in the [8] on the web. Alongside with it formalizations of Routh’s, Menelaus’ and generalized form of Ceva’s theorem itself are provided.
Sätze von Menelaos und Ceva für Vielecke im sphärischen -dimensionalen Raum
Some models of geometries and a functional equation
Some models of plane geometries and a functional equation
Součet úhlů ve čtyřstěnu
Sur un mode de transformation des figures et son application à la construction de la surface du deuxième ordre déterminée par neuf points
Sur une axiomatique métrique de la géométrie euclidienne
Systeme halbkonzentrischer Kreise der euklidischen Ebene im komplexen Gebiet.
The Beckman-Quarles theorem for mappings from to .
The Boundary at Infinity of a Rough CAT(0) Space
We develop the boundary theory of rough CAT(0) spaces, a class of length spaces that contains both Gromov hyperbolic length spaces and CAT(0) spaces. The resulting theory generalizes the common features of the Gromov boundary of a Gromov hyperbolic length space and the ideal boundary of a complete CAT(0) space. It is not assumed that the spaces are geodesic or proper
The Lehmus inequality.
The n -Point Condition and Rough CAT(0)
We show that for n ≥ 5, a length space (X; d) satisfies a rough n-point condition if and only if it is rough CAT(0). As a consequence, we show that the class of rough CAT(0) spaces is closed under reasonably general limit processes such as pointed and unpointed Gromov-Hausdorff limits and ultralimits.
Triangle inequalities from the triangle inequality.
Triangles I: Shapes.
Triangles II: Complex triangle coordinates.
Triangles III: Complex triangle functions.