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implies that if A is equidecomposable with a subset of B and B is equidecomposable with a subset of A, then A and B are equidecomposable. The Banach–Tarski...

most common version uses the concept of "equidecomposability" of polygons: two polygons are equidecomposable if they can be split into finitely many triangles...

bounded subsets of the Euclidean plane with non-empty interiors are equidecomposable with respect to the area-preserving affine maps. This has consequences...

There exists a countable subset C of the sphere S such that S\C is equidecomposable with two copies of itself. Hooper's paradox: An image with many pieces...

Christian Ludwig Gerling, who proved that two symmetric tetrahedra are equidecomposable. Gauss's letters were the motivation for David Hilbert: Is it possible...

identical squares. Tarski's circle-squaring problem challenges the equidecomposability between a square and a circle; that is, cutting the disc of a circle...

Vandenhoeck & Ruprecht, Göttingen, 1971.) Laczkovich, Miklós (1990), "Equidecomposability and discrepancy: A solution to Tarski's circle squaring problem"...

38", Fundamenta Mathematicae, 7: 381 Laczkovich, Miklos (1990), "Equidecomposability and discrepancy: a solution to Tarski's circle squaring problem"...

formulated by Farkas Bolyai: that any two simple polygons of equal area are equidecomposable. Henry Witham publishes The Internal Structure of Fossil Vegetables...

William Wallace proves that any two simple polygons of equal area are equidecomposable, later known as the Wallace–Bolyai–Gerwien theorem. Samuel Hahnemann...

deprecated parameter |citeseerx= (help) Laczkovich, M. (1990), "Equidecomposability and discrepancy; a solution of Tarski's circle-squaring problem"...

William Wallace proves that any two simple polygons of equal area are equidecomposable, later known as the Bolyai–Gerwien theorem. 27 March – Lauderdale Maule...