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M bius strip symbol
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Bach and the musical Möbius strip | tadahblog.com
It is based on work with Eric Altschuler , published in Musical Times in A musical score has basically two dimensions: pitch and time. In a one-voice musical text, for example, the pitch which corresponds to the frequency of a note is represented vertically, and performance time runs from left to right. In this line from the Kyrie eleison in a 14thth century chant book, time runs from left to right and pitch corresponds to height. Many details of musical notation have changed since those times, but the basic principles are exactly the same. Kenneth J. LaBudde Department of Special Collections.
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Easily made by twisting a strip of paper and gluing the two ends together, it is an object that only has a single surface and a single edge; Escher's ants crawling on the strip traverse all of its surface area without ever crossing an edge. Despite their long history, however, no one could predict a priori what one of these strips would look like if you were to make it from, say, a three-inch wide, inch long sheet of transparent plastic. The UCL scientists not only solved that mystery, but they also figured out the maximum width of such a strip given the length, putting to rest a question first asked more than 80 years ago.
It can be realized as a ruled surface. Its boundary is a simple closed curve, that is, homeomorphic to a circle. Some of these can be smoothly modeled in Euclidean space , and others cannot. In particular, the twisted paper model is a developable surface , having zero Gaussian curvature.