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The Optimal Paper Moebius Band

Author: Sergei Tabachnikov. Everyone knows how to make a Moebius band out of a paper rectangle: give it a $180^{\circ}$ twist and attach the ends to each other. It is easy to do if the rectangle is long and narrow, but it is impossible if the ratio of the length to width is sufficiently small (say, equal to 1). Thus there exists a number $\lambda$ such that if this ratio is greater than $\lambda$, a paper Moebius band can be made, and if it is smaller than $\lambda$, then a paper Moebius band does not exist.

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Aperiodic Monotiles

Author: Marjorie Senechal. “A longstanding open problem asks for . . . a shape that admits tilings of the plane, but never periodic tilings. We answer this problem for topological disk tiles by exhibiting a continuum of combinatorially equivalent aperiodic polygons.”

Thus begins the abstract of the preprint “An Aperiodic Monotile,” first posted on on March 20, 2023 by David Smith, Joseph Myers, Craig Kaplan, and Chaim Goodman-Strauss ([1]). Propelled by social media, lively international Zoom gatherings, on-line science magazines, and The New York Times, the news streaked around the globe at (nearly) the speed of light.

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