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Trying to get a golden spiral from an overhead view of a helix
Posted:
Feb 18, 2005 7:14 AM


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!



