Almost hermitian geometry on six dimensional nilmanifolds
Almost-orthonormal vector systems.
Alternative Proof of Sine's Theorem on the Size of a Regular Polygon in Rn with the l...-Metric.
Altitude, Orthocenter of a Triangle and Triangulation
We introduce the altitudes of a triangle (the cevians perpendicular to the opposite sides). Using the generalized Ceva’s Theorem, we prove the existence and uniqueness of the orthocenter of a triangle [7]. Finally, we formalize in Mizar [1] some formulas [2] to calculate distance using triangulation.
Ambiguous loci of the farthest distance mapping from compact convex sets
Let be a strictly convex separable Banach space of dimension at least 2. Let K() be the space of all nonempty compact convex subsets of endowed with the Hausdorff distance. Denote by the set of all X ∈ K() such that the farthest distance mapping is multivalued on a dense subset of . It is proved that is a residual dense subset of K().
An Algorithm for Lifting Points in a Tropical Variety
An alternative definition of the notion valuation in the theory of near polygons.
An Analogue of the Pythagorean Theorem with Regualr n-Gons instead of Squares.
An axiom system for full -dimensional Euclidean geometry
We present an axiom system for class of full Euclidean spaces (i.e. of projective closures of Euclidean spaces) and prove the representation theorem for our system, using connections between Euclidean spaces and elliptic planes.
An axiom system for incidence spatial geometry.
Incidence spatial geometry is based on three-sorted structures consisting of points, lines and planes together with three intersort binary relations between points and lines, lines and planes and points and planes. We introduce an equivalent one-sorted geometrical structure, called incidence spatial frame, which is suitable for modal considerations. We are going to prove completeness by SD-Theorem. Extensions to projective, affine and hyperbolic geometries are also considered.
An axiom system for the class of groups of dilatations in Fano-Pappian affine planes
An Axiomatics for Hyperbolic Projective-Metric Planes in Terms of Lines and Orthogonality
Hyperbolic projective-metric planes, first axiomatized by R. Lingenberg [7], are shown to be axiomatizable in terms of lines and orthogonality.
An eigenvalue problem with mixed boundary conditions and trace theorems.
An elementary proof of Blundon's inequality.
An elementary proof of the Theorem of Beckmann and Quarles.
An embedding theorem of complete Kähler manifolds of positive Ricci curvature onto quasi-projective varieties.
An equivalent form of the fundamental triangle inequality and its applications.
An extension of the Erdős-Debrunner inequality to general power means.
An extremal characterization of projective planes.
An intrinsic characterization of foldings of euclidean space