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Möbius twists

A thin strip – of paper, say, or springy metal or wood – can be bent into a ring by joining its two ends.  If you don’t twist the strip, you get a simple cylindrical ring, like the hoop that holds together the staves of a wooden barrel.  But if the strip is twisted before the ends are joined, the ring that is formed has what is called a Möbius twist, named after the mid-19th century German mathematician August Ferdinand Möbius (although the form was known to the ancient Romans).  The form has some surprising properties.  A single twist of 180° will join the top edge of one end of the strip to the bottom edge of the other end, producing a one-sided loop.  That is, you can trace a continuous path along the center line of the loop, parallel to the edges, until you return to the starting point, and in doing so, you will have traveled along the center line of both the front and back side of the original strip.

The polyline circuits and their curved counterparts that are the skeletons for Bakker’s sculptures often twist as they visit points in the cubic lattice.   Möbius twists can become apparent when the skeletons are coated so their cross-sections have rectangular shapes.  The cross-sections travel like a roller coaster car on the skeleton path, sweeping through the sculpture’s circuit.  The cross-sections of the coating are varied for aesthetic interest, but also must vary so that at the beginning and end of the circuit the cross-sections match and can fuse.  

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