Dissection Problem
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content. In this context, the partitioning is called simply a dissection (of one polytope into another). It is usually required that the dissection use only a finite number of pieces. The Bolyai-Gerwien theorem states that any polygon may be dissected into any other polygon of the same ar...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content. In this context, the partitioning is called simply a dissection (of one polytope into another). It is usually required that the dissection use only a finite number of pieces. The Bolyai-Gerwien theorem states that any polygon may be dissected into any other polygon of the same area. It is not true, however, that any polyhedron has a dissection into any other polyhedron of the same volume. This process is possible, however, for any two zonohedra of equal volume.
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