Computing a Centerpoint of a Finite Planar Set of Points in Linear Time.
Concerning the order and the semi-order of n-dimensional Euclidean space
Configuration spaces and limits of voronoi diagrams
The Voronoi diagram of n distinct generating points divides the plane into cells, each of which consists of points most close to one particular generator. After introducing 'limit Voronoi diagrams' by analyzing diagrams of moving and coinciding points, we define compactifications of the configuration space of n distinct, labeled points. On elements of these compactifications we define Voronoi diagrams.
Constructing non-regular algebraic spreads with asymplecticly complemented regulization.
Construction des regulären Sieben- und Dreizehn-Ecks
Construction of a line through a given point to divide a triangle into two parts with areas in a given ratio.
Correction to "On a functional equation arising from hyperbolic geometry", Volume 21 (1980), 113-116.
Countable Decompositions of R2 and R3 .
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...
Counting all equilateral triangles in .
Counting Types of Rigid Frameworks.
Covering the plane with sprays
For any three noncollinear points c₀,c₁,c₂ ∈ ℝ², there are sprays S₀,S₁,S₂ centered at c₀,c₁,c₂ that cover ℝ². This improves the result of de la Vega in which c₀,c₁,c₂ were required to be the vertices of an equilateral triangle.
Critical configurations of planar robot arms
It is known that a closed polygon P is a critical point of the oriented area function if and only if P is a cyclic polygon, that is, P can be inscribed in a circle. Moreover, there is a short formula for the Morse index. Going further in this direction, we extend these results to the case of open polygonal chains, or robot arms. We introduce the notion of the oriented area for an open polygonal chain, prove that critical points are exactly the cyclic configurations with antipodal endpoints and derive...
Crooked planes.
Cutting circles and the Morley theorem.
Cyclic quadrangles from squares.
Cyklografie [Book]
Cylinder and horoball packing in hyperbolic space.
Das gemischte Volumen als Distribution.
Das Imaginäre in der Geometrie und das Rechnen mit Würfen. (Zweite Abhandlung)