Dimension Question: How Does Math Shrink 3-D Shapes?

[Wizardsblade]

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

 

[D H]

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. ... Anyhow I would be grateful if someone knew these answers of knows how the math was done to show this.

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.