Name: Anonymous 2008-05-13 14:58
Hyperdimensionality tiem
As we know, a cylinder can be defined in many distinct ways; first, by moving a circle parallel to itself; second, by rotating a rectangle around itself; and third, by folding it so as to connect two opposite edges. The question is, can we generalise it to n dimensions?
Suppose we want to generalise it according to the first construction method. We move the cylinder parallel to the hypothetic 4 axis and we have a 4-cylinder. It has 4 cells, 4 cylinders which form this polytope which we shall call a hypercylinder.
However, we could to generalise it according to the second definition, too. If we fold a rectangular prism in an R^4 space (assuming Euclidean geometry), it follows that the facets formed are the folded prism, and two 3-spheres. However, this definition does not comply with the first.
It seems as though that the definitions agree only for 3-cylinder.
inb4 "LOLOLOLOL THERE IS NOT 4TH DIMENSION UR DUMB"
Your turn.
As we know, a cylinder can be defined in many distinct ways; first, by moving a circle parallel to itself; second, by rotating a rectangle around itself; and third, by folding it so as to connect two opposite edges. The question is, can we generalise it to n dimensions?
Suppose we want to generalise it according to the first construction method. We move the cylinder parallel to the hypothetic 4 axis and we have a 4-cylinder. It has 4 cells, 4 cylinders which form this polytope which we shall call a hypercylinder.
However, we could to generalise it according to the second definition, too. If we fold a rectangular prism in an R^4 space (assuming Euclidean geometry), it follows that the facets formed are the folded prism, and two 3-spheres. However, this definition does not comply with the first.
It seems as though that the definitions agree only for 3-cylinder.
inb4 "LOLOLOLOL THERE IS NOT 4TH DIMENSION UR DUMB"
Your turn.