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Is a circle still considered a surface?

  1. May 22, 2012 #1
    The question asks to look for a surface and a circle is the only function which meets the conditions. Is this still considered a surface?
     
  2. jcsd
  3. May 23, 2012 #2
    If it is really true that only the circle meets the conditions then there's hardly anything to talk about here, but the

    interesting thing is, imo: what exactly is your definition of surface?
     
  4. May 23, 2012 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    No, a circle is a surface if and only if you are talking about the "general" "n dimensional surface" in which case you can think of a circle as a "1 dimensional surface". Of course, it would help a lot if you told what the "question" really is!
     
  5. May 23, 2012 #4
    The question asked for a surface which is equidistant from all points p(x,y,z) to the point (0,0,1) and the plane through z=-1
     
  6. May 23, 2012 #5

    Mark44

    Staff: Mentor

    I don't see that a circle figures into this problem at all. In the plane, a parabola is equidistant from a given fixed point and a given line. In other words, at each point P on the parabola, the distance from P to the fixed point is equal to the distance from P to the line.
     
  7. May 23, 2012 #6
    Although a circle is a perfectly good 1 dimensional surface, it's not the solution to your problem.

    I believe your problem is asking for this:
    Find all points ##(x,y,z)\in \mathbb{R}^3## such that
    $$\mathrm{distance}\left( (x,y,z) , (0,0,1) \right) = \mathrm{distance}\left( (x,y,z) , \mathrm{plane} \right) $$

    I have written it this way as to not give away the answer.
     
  8. May 23, 2012 #7
    Cool :) and I was so certain about that circle lol. Thanks a lot. I get a circular prabolloid with a and b = 2.
     
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