Tiling of a Möbius strip can be performed immediately by carrying over a tiling of a rectangle with the same two-sided surface area. However, additional tilings are possible by cutting tiles across glued edges. An example of such a tiling is the strip constructed from a rectangle consisting of two halves of a width 2 square (which are rejoined when edges are connected) separated by a square (Stewart 1997). Unfortunately, since the long top and bottom edges must be glued together, this example is not constructible out of paper. It also suffers from having the unit square share a boundary with itself. In 1993, S. J. Chapman found a tiling free of the latter defect (although still suffering from the former) which can be constructed using five squares. No similar tiling is possible using fewer tiles (Stewart 1997).
Möbius Strip Dissection
See alsoCylinder Dissection, Möbius Strip, Perfect Square Dissection, Torus Dissection
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ReferencesStewart, I. "Squaring the Square." Sci. Amer. 277, 94-96, July 1997.
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Cite this as:
Weisstein, Eric W. "Möbius Strip Dissection." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MoebiusStripDissection.html