منابع مشابه
Triangles in Euclidean Arrangements
The number of triangles in arrangements of lines and pseudolines has been object of some research Most results however concern arrangements in the projective plane In this article we add results for the number of triangles in Euclidean arrange ments of pseudolines Though the change in the embedding space from projective to Euclidean may seem small there are interesting changes both in the resul...
متن کاملArrangements of Pseudocircles: Triangles and Drawings
A pseudocircle is a simple closed curve on the sphere or in the plane. The study of arrangements of pseudocircles was initiated by Grünbaum, who defined them as collections of simple closed curves that pairwise intersect in exactly two crossings. Grünbaum conjectured that the number of triangular cells p3 in digon-free arrangements of n pairwise intersecting pseudocircles is at least 2n−4. We p...
متن کاملSimple Euclidean Arrangements with No (>= 5)-Gons
It is shown that if a simple Euclidean arrangement of n pseudolines has no (≥ 5)–gons, then it has exactly n − 2 triangles and (n − 2)(n − 3)/2 quadrilaterals. We also describe how to construct all such arrangements, and as a consequence we show that they are all stretchable.
متن کاملIdeal triangles in Euclidean buildings and branching to Levi subgroups
Let G denote a connected reductive group, defined and split over Z, and let M ⊂ G denote a Levi subgroup. In this paper we study varieties of geodesic triangles with fixed vector-valued side-lengths α, β, γ in the Bruhat-Tits buildings associated to G, along with varieties of ideal triangles associated to the pair M ⊂ G. The ideal triangles have a fixed side containing a fixed base vertex and a...
متن کاملArrangements of Lines with a Large Number of Triangles
An arrangement of lines is constructed by choosing n diagonals of the regular 2/i-gon. This arrangement is proved to form at least n(n 3)/3 triangular cells.
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1999
ISSN: 0179-5376
DOI: 10.1007/pl00009471