On 16/06/2013 07:40 PM, Nekar Xenos wrote:
> I've tried googling, but I can't find an answer: Is a Penrose Triangle a
> possible object in 4 dimensions?

The Penrose triangle is "impossible" in that it violates the rules of 
perspective.

An object in 3D space can be projected into a 2D figure. The human brain 
is well accustomed to this. The Penrose triangle suggests a 3D shape 
projected into 2D, but then it violates the expected rules.

In fact, you *can* construct various 3D shapes which yield the Penrose 
triangle if viewed from the right angle. The easiest way is to just have 
warped beams.

Now, can we build this thing in 4D? Well, that would depend on what it 
means to be a "Penrose triangle". Can we build something that, when 
somehow reduced to 2D, gives the familiar figure? Well, yes we can, but 
it depends on exactly how the dimension reduction is supposed to happen. 
There's more than one way to turn 4D into 2D.

(The same happens with 3D, incidentally. You can take an orthographic 
projection. You can do a perspective projection. And you can just cut a 
2D slice out. All these options exist for reducing 4D to 3D, and then 
again for 3D to 2D - or you can do it all in a single step...)

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