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Hinged dissection
A hinged dissection, also known as a swing-hinged dissection or Dudeney dissection, is a kind of geometric dissection in which all of the pieces are connected into a chain by "hinged" points, such that the rearrangement from one figure to another can be carried out by swinging the chain continuously, without severing any of the connections. Typically, it is assumed that the pieces are allowed to overlap in the folding and unfolding process; this is sometimes called the "wobbly-hinged" model of hinged dissection.
==History==
The concept of hinged dissections was popularised by the author of mathematical puzzles, Henry Dudeney. He introduced the famous hinged dissection of a square into a triangle (pictured) in his 1907 book The Canterbury Puzzles.〔Frederickson 2002, p.1〕 The Wallace–Bolyai–Gerwien theorem, first proven in 1807, states than any two equal-area polygons must have a common dissection. However, the question of whether two such polygons must also share a ''hinged'' dissection remained open until 2007, when Erik Demaine ''et al.'' proved that there must always exist such a hinged dissection, and provided a constructive algorithm to produce them.〔 This proof holds even under the assumption that the pieces may not overlap while swinging, and can be generalised to any pair of three-dimensional figures which have a common dissection (see Hilbert's third problem).〔 In three dimensions, however, the pieces are not guaranteed to swing without overlap.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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