Ternary spaces, media, and Chebyshev sets
Testing of convex polyhedron visibility by means of graphs
This paper follows the article by V. Medek which solves the problem of finding the boundary of a convex polyhedron in both parallel and central projections. The aim is to give a method which yields a simple algorithm for the automation of an arbitrary graphic projection of a convex polyhedron. Section 1 of this paper recalls some necessary concepts from the graph theory. In Section 2 graphs are applied to determine visibility of a convex polyhedron.
Tétraèdre dont les six arêtes sont tangentes à une même sphère
The isogonal sponges on the cubic lattice.
The additivity of the volume and Sperner's lemma
The affine bundle theorem in synthetic differential geometry of jet bundles.
The affine plane AG(2,q), q odd, has a unique one point extension.
The algebra of polytopes in affine spaces.
The application of Pluecker’s line-geometry to the study of polar properties of quadrics
The Banach-Tarski paradox for the hyperbolic plane
The Banach-Tarski paradox for the hyperbolic plane (II)
The second author found a gap in the proof of the main theorem in [J. Mycielski, Fund. Math. 132 (1989), 143-149]. Here we fill that gap and add some remarks about the geometry of the hyperbolic plane ℍ².
The Beckman-Quarles theorem for mappings from to .
The best constant for a geometric inequality.
The best constant for an algebraic inequality.
The best constants for a double inequality in a triangle.
The Betten-Walker spread and Cayley's ruled cubic surface.
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 Cayley–Menger determinant is irreducible for .
The CC-version of Stewart's theorem.
The chromatic index of cyclic Steiner 2-designs.