EuDML | Browse

Une polarité d’un plan projectif est une application, souvent involutive, envoyant un point générique sur une droite générique et réciproquement. La polarité la plus classique est la polarité par rapport à une conique, mais d’autres existent : la polarité harmonique par rapport à un triangle, les polarités par rapport à une courbe algébrique de degré supérieur, la polarité par rapport à un convexe.Dans cet article nous introduisons une notion de polarité par rapport à un triangle du plan projectif,...

Projective geometry for orthogonal groups.

D.G. James (1980)

Journal für die reine und angewandte Mathematik

Projectivities over Local Rings.

Nirmala B. Limaye (1971)

Mathematische Zeitschrift

Span in incidence structures of independent sets defined on projective space

Vladimír Slezák (2000)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Tarski Geometry Axioms – Part II

Roland Coghetto, Adam Grabowski (2016)

Formalized Mathematics

In our earlier article [12], the first part of axioms of geometry proposed by Alfred Tarski [14] was formally introduced by means of Mizar proof assistant [9]. We defined a structure TarskiPlane with the following predicates: of betweenness between (a ternary relation), of congruence of segments equiv (quarternary relation), which satisfy the following properties: congruence symmetry (A1), congruence equivalence relation (A2), congruence identity (A3), segment construction (A4), SAS (A5), betweenness...

The geometry of null systems, Jordan algebras and von Staudt's theorem

Wolfgang Bertram (2003)

Annales de l’institut Fourier

We characterize an important class of generalized projective geometries $(X, X^{'})$ by the following essentially equivalent properties: (1) $(X, X^{'})$ admits a central null-system; (2) $(X, X^{'})$ admits inner polarities: (3) $(X, X^{'})$ is associated to a unital Jordan algebra. These geometries, called of the first kind, play in the category of generalized projective geometries a rôle comparable to the one of the projective line in the category of ordinary projective geometries. In this general set-up, we prove an analogue of von Staudt’s...