Greg Egan on Nostr: nprofile1q…qq00h That the cylinders touch is a consequence of the need to make the ...
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That the cylinders touch is a consequence of the need to make the centreline of the Möbius strip form a closed loop with no sharp bends, with the helical portions of the centreline meeting the straight line portions with their tangents agreeing.
Once you choose the size of the equilateral triangle formed by the midpoints of the three cylinders, you are free to adjust the radius of the cylinders within a certain range (while changing their tilt angle to ensure that they still touch), and this will correspond to changes in the length of the centreline.
All of that is independent of the precise width of the strip. But obviously the whole construction also has to be big enough to accommodate whatever width you choose for the strip.
That the cylinders touch is a consequence of the need to make the centreline of the Möbius strip form a closed loop with no sharp bends, with the helical portions of the centreline meeting the straight line portions with their tangents agreeing.
Once you choose the size of the equilateral triangle formed by the midpoints of the three cylinders, you are free to adjust the radius of the cylinders within a certain range (while changing their tilt angle to ensure that they still touch), and this will correspond to changes in the length of the centreline.
All of that is independent of the precise width of the strip. But obviously the whole construction also has to be big enough to accommodate whatever width you choose for the strip.