On Tue, 23 Jul 2013 23:14:16 +0200, clipka <ano### [at] anonymousorg> wrote:

> Am 23.07.2013 22:06, schrieb Nekar Xenos:
>> On Mon, 22 Jul 2013 22:48:15 +0200, Nekar Xenos <nek### [at] gmailcom>
>> wrote:
>>
>> If we take a vertical 2D slice of a tin can we get a rectangle.
>> If we take a horizontal 2D slice of the same tin, we get a rectangle.
>>
>> So if we have a special shape that I will call a 4D Cylinder when taking
>> 3d slices we can get a sphere or a block depending on which direction it
>> is being sliced.
>
> Somehow my intuition tells me that depending on how you construct your  
> 4D cylinder you would either get (a) a sphere or a cylinder (by  
> extruding a 3D-sphere along the 4th dimension), or (b) a cylinder or a  
> box (by extruding a cylinder along the 4th dimension), but not what you  
> describe.
>
> After all a sphere is curved in 2 dimensions, so in order to hide all  
> curvature you'd need 2 extra dimensions, i.e. a 5D space.
>

You're right about the cylinder. I got a bit mixed up between 2 ideas.

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?

-- 
-Nekar Xenos-

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