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Dimension of the circle in the plane is 1

  1. May 13, 2012 #1
    I am becoming confused when I read in Wiki that the dimension of the circle in the plane is 1!
    It is said that the dimension of circle is 2 (in general )!
    I do not get it!
     
    Last edited: May 13, 2012
  2. jcsd
  3. May 13, 2012 #2
    Re: Dimention



    Where exactly in Wiki, or wherever, is written such a thing and in what context? Please do write down a link.

    DonAntonio
     
  4. May 13, 2012 #3
    Re: Dimention

    http://en.wikipedia.org/wiki/Dimension


    In mathematics, the dimension of an object is an intrinsic property, independent of the space in which the object may happen to be embedded. For example: a point on the unit circle in the plane can be specified by two Cartesian coordinates but one can make do with a single coordinate (the polar coordinate angle), so the circle is 1-dimensional even though it exists in the 2-dimensional plane. This intrinsic notion of dimension is one of the chief ways in which the mathematical notion of dimension differs from its common usages.
     
  5. May 13, 2012 #4
    Re: Dimention

    Please note that I have changed the first post (2 becomes 1)
     
  6. May 13, 2012 #5

    micromass

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    Re: Dimention

    The dimension should be seen as a local property. That is, we should look at fictitious inhabitants of the circle and ask them what the dimension is.
    If we ask them, then they will say us that they can only go forwards or backwards, and thus they will think that they live on some sort of line. This suggests that the dimension of the circle should be 1.
     
  7. May 13, 2012 #6

    HallsofIvy

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    Re: Dimention

    Where is that said? It is certainly wrong.

    A circle is a one dimensional closed curve imbedded in a set of dimension at least two.

    I suspect you are thinking "circle" when you mean "disk".

    A disk (the circle and the points inside the circle) is a two dimensional object.
     
  8. May 13, 2012 #7
    Re: Dimention



    You, and anybody else, shouldn't do that, as it confuses things. If you want to correct an old post add a NEW post with the correction, do

    not alter the original one.

    Anyway, with the correction nothing's wrong...under certain assumptions and definitions, of course.

    DonAntonio
     
  9. May 14, 2012 #8
    Re: Dimention

    Thank you. I am Sorry.
     
  10. May 14, 2012 #9
    Re: Dimention

    So the dimension of the sphere is 2, but the dimension of the solid sphere is 3.


    Thank you all. I got it!
     
  11. May 15, 2012 #10

    HallsofIvy

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    Re: Dimention

    The "solid sphere" is, mathematically, a "ball". A sphere is the surface of a ball.
     
  12. May 15, 2012 #11
    Re: Dimention

    There are many other people on this forum that know much more than me, I'm not informed about mathematics as much as they are but my guess is this:

    You could parametrize a circle by the polar equations:
    [itex] x = rcos(\theta) + x_0 [/itex]
    [itex] y = rsin(\theta) + y_0 [/itex]

    So you'll need only one parameter to describe a circle. Even though the result will be in the real plane because for any value of theta that function gives a point (x,y) on the circle, but one variable is enough to describe the circle in [itex]\mathbb{R}^2[/itex]. Therefore its dimension is one in the real plane. I'm just saying that intuitively, not based on any particular definitions.
     
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