In this paper we prove a simple property of isosceles triangles and give two applications: construction of third proportional line segments and construction of the inverse point with respect to a circle.

A zonotope is the Minkowski addition of line segments in Rd. The zonotope construction problem is to list all extreme points of a zonotope given by its line segments. By duality, it is equivalent to the arrangement construction problem that is to generate all regions of an arrangement of hyperplanes. By replacing line segments with convex V-polytopes, we obtain a natural generalization of the z...

A zonotope is the Minkowski addition of line segments in R. The zonotope construction problem is to list all extreme points of a zonotope given by its line segments. By duality, it is equivalent to the arrangement construction problem that is to generate all regions of an arrangement of hyperplanes. By replacing line segments with convex V-polytopes, we obtain a natural generalization of the zo...

We introduce a novel and general approach for digitalization of line segments in the plane that satisfies a set of axioms naturally arising from Euclidean axioms. In particular, we show how to derive such a system of digital segments from any total order on the integers. As a consequence, using a well-chosen total order, we manage to define a system of digital segments such that all digital seg...

The Problem: The problem is to design an autonomous mobile robot that is self-assembling from independently mobile segments. We choose a design inspired by the constitution and motion of snakes or worms. In such a construction, the body of the robot is segmented and each segment can be designed as an autonomous entity, which is able to move and couple with other segments. Several of these segme...

A visibility representation of a graph maps vertices to horizontal segments and edges to vertical segments. For a weak-visibility representation, if the vertices of the original graph are adjacent, the corresponding segments will ’see’ each other. For a strong-visibility representation, the converse is true as well. Here we present a detailed step-by-step construction of a weak-visibility repre...

We generalize β-skeletons, well-known neighborhood graphs for point sets, to sets of line segments and present algorithms for computing such skeletons, both circle and lens-based, for the entire range of β values. In particular, for β ≥ 1 the β-skeleton for a set S on n segments in the Euclidean plane can be constructed in O(nα(n) log n) time and the construction relies on the Delaunay triangul...

The automatic construction of hypertext is an important part of the hypertext authoring process. This paper presents the NHS system, a system that automatically creates links for news hypertext which is tailored to the domain of newspaper archives. The suggested framework is conceptualized with the notions of stories and threads, which are substories within a story. Threads are identified by ap...

In cells simultaneously infected with any two of the three reovirus serotypes ST1, ST2, and ST3, up to 15% of the yields are intertypic reassortants that contain all possible combinations of parental genome segments. We have now found that not all genome segments in reassortants are wild type. In reassortants that possess more ST1 than ST3 genome segments, all ST1 genome segments appear to be w...