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Points in 3D space (Related to Calculus)

  1. Oct 15, 2012 #1
    The equation for the number of possible connections between n points on a 2D plane is (n-1)*(n/2).
    What is the equation for the number of possible connections between n points on a 3D plane?
    Is it the intregal of (n-1)*(n/2)?
     
  2. jcsd
  3. Oct 16, 2012 #2

    chiro

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    Hey Vodkacannon and welcome to the forums.

    What do you mean by a connection?
     
  4. Oct 17, 2012 #3
    Hi. I hope to add good questions and discussions to this web site.

    What I mean by "how many connections" is the maximum possible number of straight line paths between two different points.

    Essentially you are creating a network of points.

    For example, given 4 points on a plane p (that do not lie directly on top of each other by the way), the number of straight lines that can connect from one point to another is 6.
    (4-1)*(4/2) = 6

    (I'm sorry this probably is in the wrong forum after all.)
     
    Last edited: Oct 17, 2012
  5. Oct 17, 2012 #4

    chiro

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    Well this is a standard combinatoric problem: you have n things in total and want to find the number of ways you can choose 2 things from those n.

    Combinations do not care about order (i.e {1,2} is the same as {2,1}) which is the property required for your lines (you don't care about the start and end points, just the connection itself) and this is given by nC2 or

    nC2
    = n!/2!(n-2)!
    = n(n-1)(n-2)!/2!*(n-2)!
    = n*(n-1)/2
     
  6. Oct 18, 2012 #5

    Mark44

    Staff: Mentor

    What do you mean by a "3D plane"? A plane is a two-dimensional object. You can have a plane in three-dimensional space, but it is still a plane.
     
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