A topological transformation in which a surface is made out of an infinitely elastic material which, however, may not be torn or cut. Using this simple prescription gives the amazing two conversions illustrated above, the first of which (Wells 1991, p. 194) untangles two interlocked rings connected by a band, and the second of which (Wells 1991, p. 194; Gardner 1997, 2001) unloops one of two rings connected by a band and threaded by a band.
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ReferencesGardner, M. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications. New York: Springer-Verlag, 1997.Gardner, M. The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems. New York: W. W. Norton, pp. 264 and 269, 2001.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, 1991.
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Weisstein, Eric W. "Pretzel Transformation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PretzelTransformation.html