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Visualizing a strange quadric surface

  1. Mar 8, 2009 #1
    Hi all,

    I am trying to visualize the following quadric surface:
    x^2 + y^2 + z^2 = z

    Could someone please help me understand what this surface looks like? I could not find an example of this one on the internet.

    Thank you.
     
  2. jcsd
  3. Mar 8, 2009 #2

    Hurkyl

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    Do some algebra to simplify it. (e.g. things like collecting similar terms, completing the square, factoring, change of variable, etc)
     
  4. Mar 8, 2009 #3
    Consider what the surface
    (x-a)^2 + (y-b)^2 + (z-c)^2 = d

    looks like
     
  5. Mar 9, 2009 #4
    (x-a)^2 + (y-b)^2 + (z-c)^2 = d is a sphere centered at a, b, c with radius square root of d.

    Now regarding the first post, I can bring the z over to the left hand side:

    x^2 + y^2 + z^2 - z = 0

    Then complete the square

    x^2 + y^2 + (z - 1/2)^2 -1/4 = 0
    [(z - 1/2)^2 = z^2 - 2*1/2 z + 1/4]

    Then

    x^2 + y^2 + (z-1/2)^2 = 1/4

    This means that this is a sphere centered at 0,0, 1/2. Is that correct?
     
  6. Mar 9, 2009 #5

    mathman

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    Yes and the radius is 1/2.
     
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