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Thread: Cartesian formula for Archimedean Sprial please

  1. September 7th 2009, 03:31 PM #1
    rainer
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    Cartesian formula for Archimedean Sprial please

    The formula for graphing an Archimedean spiral is always given in polar coordinates. I need to know the formula in Cartesian coordinates (x,y). Can anyone help? Thanks.
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  2. September 7th 2009, 03:38 PM #2
    Chris L T521
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    Quote Originally Posted by rainer View Post
    The formula for graphing an Archimedean spiral is always given in polar coordinates. I need to know the formula in Cartesian coordinates (x,y). Can anyone help? Thanks.
    It's an implicit equation that you can't solve for y.

    So if r=a+b\theta,\,a,b\in\mathbb{R}, then by conversion to rectangular coordinates, we have \sqrt{x^2+y^2}=a+b\tan^{-1}\left(\tfrac{y}{x}\right)

    We can't simplify this any further...
    Last edited by Chris L T521; September 7th 2009 at 03:41 PM. Reason: used wrong spiral equation... ><
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