Date: Feb 18, 2005 7:14 AM
Author: Jon Miller
Subject: Trying to get a golden spiral from an overhead view of a helix

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!