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Parametric representation of a Spiral

  1. Sep 22, 2010 #1
    Propose a parametric representation of a spiral.
    Hint: Use the parametric representation of a circle.

    This is the parametric representation of a circle we are given :

    x = r * Cos(Theta)
    y = r * Sin (Theta)

    0 <= Theta <= 2 Pi

    Nope, we are not given anything background on spirals.

    I am like super new at this graphics thingy. I've been searching around the net for 4 hours now, I did find a few answers but none taught me how to get the representation from a circle and I have no idea how they derive at the answer.

    All I know right now about this graphics thingy is :

    x and y are like coordinates.

    And that t or Theta in this case is kinda like a path or timeline where decides when coordinates of x and y starts and ends.

    I am thinking of making the radius a parameter and then slowly increasing it?

    x = u * Cos(Theta)
    y = u * Sin (Theta)

    1 <= u <= 4

    Something like that?

    Thats all I know, so help please?
     
    Last edited: Sep 22, 2010
  2. jcsd
  3. Sep 22, 2010 #2

    lanedance

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    Homework Helper

    that would work as a 2D spiral, but you would want it all in terms of one parameter, so try starting with theta(u) = u
     
  4. Sep 22, 2010 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    If u is fixed, that is a circle of radius u, not a spiral. If u is a variable, then you have two parameters and that is a surface, not a spiral.

    To get a spiral in two dimensions, you need to make the radius variable but not introduce a new variable so something like x= theta*cos(theta), y= theta* sin(theta).

    If the problem is, as lanedance suggests, a three dimensional spiral, a "helix", then you need to introduce a "z" component that increases, again not introducing a new parameter.

    Something like x= Cos(Theta), y= Sin(Theta), z= Theta.

     
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