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Dimension Question.

  1. Jan 4, 2006 #1
    I remember when I was in school my professor mathematically shrank a cube to a point and when he did so it was a sphere. So I was wondering does this mean that a sphere is the best way to think 3-D. Then I also wondered what would a square shrink to, I would guess a circle but I do not remember how he did this. Then I thought about a line... would it turn out to be a vector or would it stay a line? Anyhow I would be grateful if someone knew these answers of knows how the math was done to show this.
    Thanks
     
  2. jcsd
  3. Jan 4, 2006 #2

    D H

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    A point is a zero-dimensional object. It is not a line segment, a circle, or a sphere, or any other dimensioned object. It is mathematically invalid to speak of a point as being a sphere since a sphere has a non-zero radius by definition. For that matter, it is mathematically invalid to speak of a point as being any dimensioned object. Your professor was playing games with degeneracies.
     
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