the same motif from two measures earlier. Because of this symmetry, this canon can be thought of as having its score written on a Möbius strip. In music theory, tones that differ by an octave are generally considered to be equivalent notes, and the space of possible notes forms a circle, the chromatic circle. Because the Möbius strip is the configuration space of two unordered points on a circle, the space of all two-note chords takes the shape of a Möbius strip. This conception, and generalizations to more points, is a significant application of orbifolds to music theory. Modern musical groups taking their name from the Möbius strip include American electronic rock trio Mobius Band and Norwegian progressive rock band Ring Van Möbius. Möbius strips and their properties have been used in the design of stage magic. One such trick, known as the Afghan bands, uses the fact that the Möbius strip remains a single strip when cut lengthwise. It originated in the 1880s, and was very popular in the first half of the twentieth century. Many versions of this trick exist and have been performed by famous illusionists such as Harry Blackstone Sr. and Thomas Nelson Downs. See also Möbius counter, a shift register whose output bit is complemented before being fed back into the input bit Penrose triangle, an impossible figure whose boundary appears to wrap around it in a Möbius strip Ribbon theory, the mathematical theory of infinitesimally thin strips that follow knotted space curves Smale–Williams attractor, a fractal formed by repeatedly thickening a space curve to a Möbius strip and then replacing it with the boundary edge Umbilic torus, a three-dimensional shape with its boundary formed by a Möbius strip, glued to itself along its single edge Notes References External links Topology Recreational mathematics Surfaces