Hypercylinder

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.

>>1
Racist.

>>2
wat

>>2
I agree.

Kill yourself.  When talking about hyperdimensional objects, there are ONLY two definitions for a three dimensional cylinder, all the others just happen to be ways you can "make" one.

>cylinder
>A three dimensional hypercylinder that can roll along one linear axis. It can be formed by extending a circle into realmspace, or by rotating a square into realmspace.

>hypercylinder
>An n-dimensional cylinder. Hypercylinders are formed by extending or rotating lower-dimensional hypercylinders into higher dimensional space. In realmspace there is only one hypercylinder, the cylinder. In tetraspace, there are two hypercylinders: the cubinder and spherinder.

>cubinder
>A four dimensional hypercylinder that can roll along one axis, but is flat on all the other sides. It can be formed by extending a cylinder into tetraspace linearly.

>spherinder
A four dimensional hypercylinder that can roll around in a planar region. It can be formed by extending a sphere into tetraspace linearly.

there could be more then 3-dimensions but only if you are one of three things.

1. mathematician
2. theoretician
3. a screenwriter

if their are less thin three it is not perceivable, if it has more you could not tell.

>>6

4. psyker

>>4

5. John Titor

>>8

I think I see what you did there

>>5
>When talking about hyperdimensional objects
>for a three dimensional cylinder

wat

>>10
*facepalm*
A cylinder is a 3-dimensional hypercylinder, retard. Hypercylinder being a sort of "meta-object" and a "regular cylinder"/3-cylinder being that object represented in 3-space.

If D is a disk and L is a line, the product set DxL is a cylinder. The natural generalizition seems to me to be either the product of a sphere and a line, or the product of a rectangle and a disk.