What would be a simple mathematical function that produces the following spiral?
The set below describes a series of points (azimuth and radius from an
origin of 0,0) that, when connected, defines a spiral.  It looks great
on graph paper.  However I'm not sure where to start in terms of creating
a reproduction of this in a computer program.  I want something more
than just an abstract formula... I need a methodology for recreating
this spiral.  My math is not that good, but if you show me how, I can
make it work.

AZIMUTH   RADIUS
(deg)
010       13000
020       12500
030       12000
040       11550
050       11100
060       10650
070       10250
080        9850
090        9450
100        9100
110        8750
120        8400
130        8100
140        7800
150        7500
160        7200
170        6950
180        6700
190        6450
200        6200
210        5950
220        5750
230        5550
240        5350
250        5150
260        4950
270        4800
280        4650
290        4500
300        4350
310        4200
320        4050
330        3900
340        3750
350        3650
000        3550
010        3450
020        3350
030        3250
040        3150
050        3050

Hello mjsmigel:

Thanks for the interesting question. I will try to answer it for you.
If I'm not quite getting what you're after, please ask me for
clarification and I'll do my best to clear things up for you.

Spirals are fascintating shapes that are typically represented (in
math) in what are called polar coordinates. That is, instead of the
typical (cartesian) coordinates, where you have an "x" and a "y"
value, you instead have an "r" value (for radial distance - distance
from the center) and a "t" or "theta" value (for angle - in radians,
as opposed to degrees). Your data is already in polar coordinates, so
that's a good start.

I used Maple (a mathematical computing program) to try to model your
data as closely as possible with a "simple mathematical function."
After several tries. the closest formula I could get to your data was:

r = 580000/t^2, as t varies from 6.46..13.45 *radians*

Again, to demonstrate that this is a pretty close approximation, I
plotted both your original set of data (the black line) and the above
formula (the green line) together on one set of axes. Have a look at:

http://www.lucidmatrix.com/uploads/spiral.jpg 

Of course, if you want to produce more "loops" in the spiral, you only
need change (increase) the range over which t varies.

Now, if you want to try to reproduce this spiral in a computer
program, I'd suggest converting from polar coordinates into cartesian
coordinates. To do so, first compute the r and t values from the above
formula, then you can produce the x and y values using:

x = r Cos[t]
y = r Sin[t]

as can be seen on 

Drawing Spirals on Your Computer
URL: http://mathforum.org/library/drmath/view/54401.html


I hope this information helps with your research.              
              
If you need any clarification of the information I have provided,
please ask using the clarification feature and provide me with
additional details as to what you are looking for. As well, please
allow me to provide you with clarification(s) *before* you rate this
answer.
              
Thank you.               
              
websearcher-ga               
              
              
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spiral formula
http://mathforum.org/library/drmath/view/54401.html

Excellent answer... I don't have any questions at all.  The sample
graphic really drove the point home.  Thank you!