Drawing Spirals on Your Computer

Date: 9/5/95 at 4:17:24
From: Anonymous
Subject: Spiral formula(s)

Hello !

I want to draw spirals with the computer. I don't know how.
Can you send me which formula(s) I can use to do it.
If possible it will be easier for me to use Cartesian formulas.
Thank you in advance.

Fabrice Bailly

Date: 9/6/95 at 12:18:1
From: Doctor Ken
Subject: Re: Spiral formula(s)

Hello!

I think the easiest way to think about spirals is in polar coordinates, and
then you can convert to cartesian coordinates in your program.  In polar
coordinates, you can have the angle just go from 0 to as big as you want
depending on how many times around you want to go, and then you can have 
the radius be some function of x that gets bigger as x gets bigger.  One of the
simplest functions you could use is F(x) = x.  You could also use x^2, or
Sqrt{x}, or whatever.  If you want something funky, try F(x) = x * Sin(x), 
and make sure that your Sine is in radians.

To convert from polar coordinates to Cartesian, use the conversion
x = r Cos[t]
y = r Sin[t].

-Doctor Ken,  The Geometry Forum