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Closed plane curve

  1. Sep 18, 2013 #1
    1. The problem statement, all variables and given/known data

    How can I draw a closed plane curve with positive curvature that is not convex

    3. The attempt at a solution

    I was thinking drawing it like a banana but more curved, will that do?
     
    Last edited: Sep 18, 2013
  2. jcsd
  3. Sep 18, 2013 #2

    haruspex

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    Is it allowed to cross itself?
     
  4. Sep 18, 2013 #3
    since it is not convex I think it can cross itself.
     
  5. Sep 18, 2013 #4

    Ray Vickson

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    A banana curve does not have positive curvature everywhere.
     
  6. Sep 18, 2013 #5
    Ray - You are right! So how can I draw one that is positive curvature?
     
  7. Sep 18, 2013 #6

    Ray Vickson

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    Well, that is your assignment!
     
  8. Sep 18, 2013 #7
    Can you give a hint please?
     
  9. Sep 18, 2013 #8
    If it were convex then it is just a sphere? But a non-convex with positive curvature is confusing me.
     
  10. Sep 18, 2013 #9

    LCKurtz

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    You mean "circle". You were given a hint -- let the curve cross itself. Try it.
     
  11. Sep 18, 2013 #10
    Yup, I am meant circle. Will an number 8 satisfy it where the top is a bit more curved?
     
  12. Sep 18, 2013 #11

    LCKurtz

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    No. As soon as you start curving the other way your curvature goes through zero.
     
  13. Sep 18, 2013 #12
    Wow, this is harder than I thought.
     
  14. Sep 18, 2013 #13
    So it must cross itself? Am I overthinking this?
     
  15. Sep 18, 2013 #14

    LCKurtz

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    It isn't hard; it's almost trivial. Take a pencil and start drawing. Don't change curvature direction, use the hint, and close the curve.
     
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