Titlebook: New Trends in Intuitive Geometry; Gergely Ambrus,Imre Bárány,János Pach Book 2018 Springer-Verlag GmbH Germany, part of Springer Nature 20

Cosmopolitan

偏见

粘土

The Topological Transversal Tverberg Theorem Plus Constraints, lemma to show how one can obtain many new topological transversal theorems of Tverberg type. In particular, we derive a topological generalized transversal Van Kampen–Flores theorem and a topological transversal weak colored Tverberg theorem.

高原

,On the Volume of Boolean Expressions of Balls – A Review of the Kneser–Poulsen Conjecture,t the distances between the centers of the balls do not increase, then the volume of the union of the balls does not increase as well. Our goal is to give a survey of attempts to prove this conjecture, to discuss possible generalizations, and to collect some relevant open questions.

路标

,A Survey of Elekes-Rónyai-Type Problems,rge image on a Cartesian product ., unless . has a group-related special form. We discuss this problem and a number of variants and generalizations. This includes the Elekes-Szabó problem, which generalizes the Elekes-Rónyai problem to a question about an upper bound on the intersection of an algebr

Madrigal

The Geometry of Abrasion,rical theory for the abrasion of a single particle under collisions and extend it to include mutual abrasion of two particles and also frictional abrasion. Next we review the heuristically simplified box model [.], operating with ordinary differential equations, which also describes mutual abrasion

thalamus

Computing Upper Bounds for the Packing Density of Congruent Copies of a Convex Body,m is a generalization of the linear programming bound for sphere packings. We illustrate its use by computing an upper bound for the maximum density of packings of regular pentagons in the plane. Our computational approach is numerical and uses a combination of semidefinite programming, sums of squa

Irrigate

Two Geometrical Applications of the Semi-random Method,endent set in hypergraphs with certain uncrowdedness properties. The first geometrical application was a major achievement in the history of Heilbronn’s triangle problem. It proved that the original conjecture of Heilbronn was false. The semi-random method was extended and applied to other problems.

侵略

,Erdős–Szekeres Theorems for Families of Convex Sets,e subset in convex position. This classical result has been generalized in several directions. In this article we review recent progress related to one such direction, initiated by Bisztriczky and Fejes Tóth, in which the points are replaced by convex sets.

外星人