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Spiral around cone

  1. Nov 7, 2009 #1
    I am looking for the formula to describe a spiral formed around a conical shape. If any particular details are needed, please make them variables and define them.

    Thanks to all for the help!
  2. jcsd
  3. Nov 7, 2009 #2


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    Hi eli_lied! :smile:

    Do you mean a shortest-possible-distance spiral, as if a string was pulled tight around the cone?

    If so, then remember a cone's "own" geometry (as opposed to embedded geometry) is flat Euclidean …

    so just cut the cone along a generator, unfold it, draw a straight line on it, and then join it up again. :wink:
  4. Nov 7, 2009 #3
    Thanks for the reply Tiny Tim :)

    What I'm specifically looking for is the equation for a "spring-like" spiral that is, for lack of a better term, 0 at one end and infinity at the other. As though a spring were wrapped around a conical formation with a varying height that increases over time.
  5. Nov 7, 2009 #4
    The simplest method would be to use a parametric equation

    [tex] r(t)=(x(t), y(t), z(t)): x(t)=t \sin t, y(t)=t \cos t, z(t)=t [/tex]

    or something like that.
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