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Preface
The index of an isometric embedding
Maximal ot-subsets of the Euclidean plane
The cardinalities of at-sets in a real Hilbert space
Isosceles triangles and it-sets in Euclidean space
Some geometric consequences of Ramsey’s combinatorial theorem
Convexly independent subsets of infinite sets of points
Homogeneous coverings of the Euclidean plane
Three-colorings of the Euclidean plane and associated triangles of a prescribed type
Chromatic numbers of graphs associated with point sets in Euclidean space
The Szemerédi–Trotter theorem and its applications
Minkowski’s theorem, number theory, and nonmeasurable sets
Tarski’s plank problem
Borsuk’s conjecture
Piecewise affine approximations of continuous functions of several variables and Caratheodory–Gale polyhedra
Dissecting a square into triangles of equal areas
Geometric realizations of finite and infinite families of sets
A geometric form of the Axiom of Choice
Convex sets in real vector spaces
Real-valued convex functions
The Principle of Inclusion and Exclusion
The Erdös–Mordell inequality
Some facts from graph theory
Bibiliography
Index