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Hinged dissection

Loop animation of hinged dissections from triangle to square, then to hexagon, then back again to triangle. Notice that the chain of pieces can be entirely connected in a ring during the rearrangement from square to hexagon.

In geometry, a hinged dissection, also known as a swing-hinged dissection or Dudeney dissection,[1] 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.[2] Typically, it is assumed that the pieces are allowed to overlap in the folding and unfolding process;[3] this is sometimes called the "wobbly-hinged" model of hinged dissection.[4]

  1. ^ Akiyama, Jin; Nakamura, Gisaku (2000). "Dudeney Dissection of Polygons". Discrete and Computational Geometry. Lecture Notes in Computer Science. Vol. 1763. pp. 14–29. doi:10.1007/978-3-540-46515-7_2. ISBN 978-3-540-67181-7.
  2. ^ Pitici, Mircea (September 2008). "Hinged Dissections". Math Explorers Club. Cornell University. Retrieved 19 December 2013.
  3. ^ O'Rourke, Joseph (2003). "Computational Geometry Column 44". arXiv:cs/0304025v1.
  4. ^ "Problem 47: Hinged Dissections". The Open Problems Project. Smith College. 8 December 2012. Retrieved 19 December 2013.

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