A 2-metric Characterization of the Euclidean Plane.
A Characterization of Motions as Bijections Preserving Inradius or Circumradius One.
A consistency equation for three geometries.
A new geometric inequality.
A normed space with the Beckman-Quarles property.
A projective characterization of cyclicity.
A supplement to Eddy's paper.
A Sylvester Theorem for Conic Sections.
Affine and projective generalization of Wallace lines.
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 upper bound for a sequence of cevian inequalities.
Angle-preserving transformations of spheres.
Application de la généralisation du principe de correspondance à la théorie de l'élimination
Approximation eines Evolventenstücks durch ein Kreisbogenstück
B. Pivot theorems in n-space
Bounds for quaternionic line systems and reflection groups.
Certain inequalities concerning bicentric quadrilaterals, hexagons and octagons.
Coincidences of simplex centers and related facial structures.
Concerning the order and the semi-order of n-dimensional Euclidean space
Countably convex sets
We investigate countably convex subsets of Banach spaces. A subset of a linear space is countably convex if it can be represented as a countable union of convex sets. A known sufficient condition for countable convexity of an arbitrary subset of a separable normed space is that it does not contain a semi-clique [9]. A semi-clique in a set S is a subset P ⊆ S so that for every x ∈ P and open neighborhood u of x there exists a finite set X ⊆ P ∩ u such that conv(X) ⊈ S. For closed sets this condition...