Am 24.07.2013 20:54, schrieb Nekar Xenos:

> I want to find a 4d object that has a cube slice in one place and a
> sphere slice in another place.
>
> So I'll start with 2d slices from 3d objects. 3 dimensional space is
> made up of 2-d planes stacked on top of each other. The top plane of the
> object is a square. The next layer is slightly curved. Each layer is
> more curved than the previous. The bottom layer is a perfect circle. The
> one side is round and the other side still has corners. An unfinished
> table leg on a lathe :)
>
> So shifting the dimensions up we get a cube on the first 3d section of
> this "4d table leg" with each cube being curved more than the previous
> and the last 3d section is a perfect sphere.
>
> On the first object we can see that the first and last 2d sections look
> totally different. But because we can see the whole object, it doesn't
> seem strange to us. But because we cannot see into the 4d realm the 4d
> table leg can look like a cube if we see the first slice or a sphere if
> we see the last slice.
>
> Is this correct now?

Spot-on.

You might imagine a sphere morphing into a cube over time, with time 
being the 4th dimension in that picture.

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