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!