منابع مشابه
Halving Lines and Underlying Graphs
In an Apollonian circle packing, the curvatures a, b, c, d of any four mutually tangent circles satisfy Descartes’ equation, 2(a + b + c + d) = (a+ b+ c+ d). For an equilateral triangle and a point P , if a, b, c, d denote the squares of the lengths of the sides of the triangle and the distances from P to the vertices of the triangle, then a, b, c, d, satisfy 3(a+ b+ c+d) = (a+ b+ c+d). Define ...
متن کاملAn Improved, Simple Construction of Many Halving Edges
We construct, for every even n, a set of n points in the plane that generates Ω ne √ ln 4· √ ln n/ √ ln n halving edges. This improves Tóth’s previous bound by a constant factor in the exponent. Our construction is significantly simpler than Tóth’s.
متن کاملRederiving the Upper Bound for Halving Edges using Cardano's Formula
In this paper we rederive an old upper bound on the number of halving edges present in the halving graph of an arbitrary set of n points in 2-dimensions which are placed in general position. We provide a different analysis of an identity discovered by Andrejak et al, to rederive this upper bound of O(n). In the original paper of Andrejak et al. the proof is based on a naive analysis whereas in ...
متن کاملHalving Lines and Their Underlying Graphs
In this paper we study underlying graphs corresponding to a set of halving lines. We establish many properties of such graphs. In addition, we tighten the upper bound for the number of halving lines.
متن کاملOn $(\le k)$-edges, crossings, and halving lines of geometric drawings of Kn
Let P be a set of points in general position in the plane. Join all pairs of points in P with straight line segments. The number of segment-crossings in such a drawing, denoted by cr(P ), is the rectilinear crossing number of P . A halving line of P is a line passing though two points of P that divides the rest of the points of P in (almost) half. The number of halving lines of P is denoted by ...
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ژورنال
عنوان ژورنال: Involve, a Journal of Mathematics
سال: 2018
ISSN: 1944-4184,1944-4176
DOI: 10.2140/involve.2018.11.1