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Polar curves

  1. May 13, 2014 #1
    dimples.png


    Why doesn't r = a(1+cosθ) have a dimple? I mean p=1, q=1 so q≤ p<2q and therefore r = a(1+cosθ) should have a dimple (like the curve in the bottom right corner of the image above)?
     
  2. jcsd
  3. May 13, 2014 #2

    LCKurtz

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    It does have a dimple with a point. If q gets any smaller it loops inside itself.
     
  4. May 14, 2014 #3
    Is that considered to be a dimple? I thought dimples have a ''flat'' shape to them like the curve in the box on the bottom right?

    Also, according to this page:

    http://www.jstor.org/discover/10.2307/3026536?uid=3738032&uid=2&uid=4&sid=21104158779553

    A cardioid doesn't have a dimple? (Table 1)

    Thanks
     
  5. May 14, 2014 #4

    haruspex

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    Whether the cusp of a cardioid is regarded as a degenerate loop, a degenerate dimple, or distinct from both, doesn't strike me as terribly important. If I tell you a curve is an ellipse, does that mean it's not a circle?
     
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