On 8/31/2012 10:53 AM, Allan Wechsler wrote: Don't cut the pieces out of a hollow cylinder. Cut them out of a solid cylinder. I bet George Hart can just print out the pieces for you...
You still get two helices, with no solid core because the "C scale" and "D scale" pieces meet each other at the axis. I think it would still be springy enough to cause excessive error, unless it were solid diamond or tungsten (-:, and you still have to solve the axis alignment problem (making sure the two helices remain co-axial) which is much more easily solved by the transparent concentric hollow cylinder solution that I mentioned at the end. On 8/31/12, George Hart <george@georgehart.com> wrote:
[...] A cursorless helical slide rule that doesn't "spring" could be designed using a two-color process to make the inner cylinder solid with the scale of a contrasting color, and the outer (hollow) cylinder using a clear material for its background color. (The scale markings could be above the line for one and below the line for the other.) However, the technology is not yet as accurate and inexpensive as one would like for two-color 3D-printing processes.
Wow, 3-D printing the whole thing, that's an approach I wasn't willing to consider. I'd be asking how we make the end product snug enough to keep the two helices co-axial. Clearly you'd print them as two pieces, smooth off the mating surfaces, then screw then together -- but how do you smooth the inner surface of the transparent outer piece, whilst keeping it transparent? I guess I'm getting rather far afield of math-fun here, unless we start citing relevant formulas. -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com