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Ed Wall
Posts:
843
Registered:
12/3/04


Re: Trying to get a golden spiral from an overhead view of a helix
Posted:
Feb 18, 2005 2:56 PM


Interesting question. Perhaps you might say something in a bit more detail on how other logarithmic spirals are approximated by helix projections. Enneper, I think, showed that the projection of a helix on a cone was a logarithmic spiral, but I'm not sure of the cite.
Ed Wall
>Hi, I wonder if someone could help me with a project I'm working on. >It's a perspective drawing with what I hope are interesting geometric >underpinnings, but which are a bit beyond me, unfortunately. Here's >the situation. The viewer or camera or whatever is looking right down >the central axis of a helix. It's my understanding that if you're >looking right down the central axis, a 2d representation of the helix >would approximate a logarithmic spiral. If it's a perspective and not >an orthographic drawing, that is. I'm going for one logarithmic spiral >in particular, what I think is called a golden spiral. The one shown >here: > >http://www.levitated.net/daily/levGoldenSpiral.html > >Now, it seems to me that the two properties of the helix that I can >adjust to make it appear that way are its radius and the distance >between its loops or coils. (Sorry, part of the problem is that I >don't really know the vocabulary.) My question is, can anyone help me >figure out what those two attributes of the helix should be, relative >to each other, for the view I'm describing to come as close as >possible to a golden spiral? Would it be the golden ratio or >something? > >Finally, the entry for logarithmic spiral on MathWorld... > >http://mathworld.wolfram.com/LogarithmicSpiral.html > >...has something about approximating a logarithmic spiral by starting >with equally spaced rays and drawing a perpendicular from one to the >next. That would seem to relate, but I just can't get my head around >it. Thanks so much for any help you can give me!



