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What (who) is dissection$22135$ - definition
![A reconstruction of the vertebral arteries from a CT scan, seen from the front. From the bottom, V1 is from the subclavian artery to the foramina, V2 is from the foramina to the second vertebra, V3 is between the foramina until entry into the skull, and V4 is inside the skull embedded in the [[dura mater]]. They merge into the basilar artery, which then divides into the [[posterior cerebral artery]].](https://commons.wikimedia.org/wiki/Special:FilePath/Vertebral artery 3D AP relabeled.jpg?width=200 "A reconstruction of the vertebral arteries from a CT scan, seen from the front. From the bottom, V1 is from the subclavian artery to the foramina, V2 is from the foramina to the second vertebra, V3 is between the foramina until entry into the skull, and V4 is inside the skull embedded in the [[dura mater]]. They merge into the basilar artery, which then divides into the [[posterior cerebral artery]].")
Wikipedia
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. Additionally, to avoid set-theoretic issues related to the Banach–Tarski paradox and Tarski's circle-squaring problem, the pieces are typically required to be well-behaved. For instance, they may be restricted to being the closures of disjoint open sets.
The Bolyai–Gerwien theorem states that any polygon may be dissected into any other polygon of the same area, using interior-disjoint polygonal pieces. It is not true, however, that any polyhedron has a dissection into any other polyhedron of the same volume using polyhedral pieces (see Dehn invariant). This process is possible, however, for any two honeycombs (such as cube) in three dimension and any two zonohedra of equal volume (in any dimension).
A dissection into triangles of equal area is called an equidissection. Most polygons cannot be equidissected, and those that can often have restrictions on the possible numbers of triangles. For example, Monsky's theorem states that there is no odd equidissection of a square.
