Titlebook: Research Problems in Discrete Geometry; Peter Brass,William O. J. Moser,János Pach Textbook 2005 Springer-Verlag New York 2005 Lattice.com

ethereal

叙述

Problems on Repeated Subconfigurations,lence relation. The basic questions discussed in Chapter 5 are to determine the size of the largest equivalence class and the number of distinct equivalence classes. Erdős and Purdy [.], [.] started the investigation of the same questions for .-dimensional simplices in IR., that is, for (. + 1)-tupl

coagulate

思想灵活

Problems on Points in General Position,equire that no three elements be collinear can usually be described as problems on .. The order type is an equivalence relation on sets of . points in the plane, no three collinear, in which two sets . are equivalent if and only if there is a bijection .: . → . between the points such that each tria

Cloudburst

Cognizance

语源学

Geometric Inequalities,very old result that has been generalized in many directions. Apart from the fact that one does not need convexity here, essentially the same result holds in all scenarios in which the notions of “perimeter” and “area” can be naturally defined. The embedding space can also be varied: similar inequal

pantomime

可用

Distance Problems,ng points to coincide would destroy the geometric aspect of the problem and essentially reduce it to a graph-theoretic problem. Given any point set ., we can define its so-called ., connecting two elements of . by an edge if and only if their distance is one.

芳香一点

Geometric Inequalities,erimeter and the area. For the extensive literature on the many aspects of these problems see [.], [.], [.], [.], [.], [.]. In this section, we concentrate on isoperimetric problems in discrete geometry, and avoid most questions that largely belong to convexity, differential geometry, or geometric measure theory.