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Difference equation help.

  1. May 14, 2005 #1
    Ok, Im not sure if this is the right section, but seeing that difference equations are the discrete version...

    Now the question is :
    Into how many regions do n simple ovals divide the plane, given that every oval meets every other oval in two points and no point in the plane is common to more than two ovals.

    I have NO idea how to go about this. Anyone care to shed some light?
  2. jcsd
  3. May 16, 2005 #2
    Any ideas at all? Is this the right section?
  4. May 16, 2005 #3


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    Are you sure this is the full question and doesn't have any other parts? What sort of work have you been doing recently on this topic? I'm just trying to get some context because the question doesn't seem very full.
  5. May 16, 2005 #4


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    Looks to me like an induction question. Two ovals, meeting in two points, divide the plane into 4 regions. 3 ovals, each meeting each other in two points, divide the plane into 9 regions. Hmm, should we guess n2? I suspect you can find a difference equation relating the value for n ovals with the value for n+1 ovals.
  6. May 17, 2005 #5
    Thanks for the replies guys. :D

    Halls, what would be some of the steps involved in setting up these types of equations? We have covered how to solve them, but not how to set them up. Which is what Im having trouble with.
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