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Math Help - True or false, limits curvature

  1. #1
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    True or false, limits curvature

    True or False: Let Kr be the curvature of a circle of radius r (in R2) then lim as r approaches infinity Kr=1.

    I say false because as r approaches infinity the Kr= infinity.
    Is that right?
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  2. #2
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    On a circle of radius r, the curvature is uniformly \frac{1}{r}.

    We know this because the curvature on the unit circle is uniformly 1, and on an arc-length-paramatrized circle of radius r, \mathbf{p'}(s) changes 1/r as fast.
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  3. #3
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    so the lim kr as r approaches infinity would = 0 not infinity, correct? so Its false still
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  4. #4
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    That is correct.
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