On 8/31/2012 7:33 PM, Bill Gosper wrote:
A few G4s ago, someone exchange gifted 3D-printed helic(oid)ally bisected screw-apart sintered plastic cubes. It would be interesting to determine the dimensions, for a given pitch, of a helic(oid)ally bisected cylinder that maximize torsional stiffness.
That was me. My G4G8 exchange item was: http://georgehart.com/puzzles/cube-puzzle.html I optimized the dimensions for solution difficulty. With too tight a pitch, it looks like a screw, and people figure out right away to screw the parts together. With too slow a pitch, it is easy to assemble the parts "from the side" instead of screwing them together. In between is an optimum of difficulty, which I worked out with some experiments.
I don't understand the need for a transparent slide rule component, except for maybe a sleevelike cursor.
I agree there's no absolute need. I was proposing the outside cylinder be transparent, except for embedded markings, because having it solid gets around the stiffness questions of the coiled spring. Geometrically, both cylinders would be completely smooth at their interface surface. I do not want to have to screw the scales along each other. It would take forever to move from one end of a long helix to the other. Free movement of the two scales is desirable "across the threads" so it is quick and easy to line up any desired values on the C and D scales. George http://georgehart.com/