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Currently displaying 1 – 9 of 9

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Equidecomposability and discrepancy; a solution of Tarski's circle-squaring problem

M. Laczkovich — 1990

Journal für die reine und angewandte Mathematik

Decomposition of Convex Figures into Similar Pieces.

M. Laczkovich — 1995

Discrete & computational geometry

On Kemperman's inequality 2f(x)≤ f(x+h)+f(x+2h)

M. Laczkovich — 1984

Colloquium Mathematicae

Equidecomposability of Jordan domains under groups of isometries

M. Laczkovich — 2003

Fundamenta Mathematicae

Let $G_{d}$ denote the isometry group of $ℝ^{d}$ . We prove that if G is a paradoxical subgroup of $G_{d}$ then there exist G-equidecomposable Jordan domains with piecewise smooth boundaries and having different volumes. On the other hand, we construct a system $ℱ_{d}$ of Jordan domains with differentiable boundaries and of the same volume such that $ℱ_{d}$ has the cardinality of the continuum, and for every amenable subgroup G of $G_{d}$ , the elements of $ℱ_{d}$ are not G-equidecomposable; moreover, their interiors are not G-equidecomposable...