Continuing yesterday’s theme of higher dimensions, in this post I look at a couple more 4 Dimension shapes and how they can be represented on a screen.
Thinking about how to show 4 dimensions its helpful to think of ways to show 3 dimensions on a 2D screen. One such way is to take ‘cross sections’. For example, one way to show a cylinder is a series of circles. Stack these together and you get a cylinder.
A cross section of a 4 Dimension shape will be a 3 Dimension shape,
Another way of thinking of this is to consider time as the forth dimension*. Imagine seeing a sphere appearing as a dot, then growing to ‘full size’, then disappearing again at the same rate. The diagram here would show stages of the process.
I’ve seen other representations of a ‘hypersphere’ but this is the one clearest to me.
How would a ‘Hypercube’ look like, using the same ‘cartoon technique?
(*Some people think this to be the case, through the 4-Dimension space-time physicists work with isn’t that simple, but it will do for this thought experiment).
Before we move off 4-Dimension shapes, I’d like share one of my favourite shapes. This can only exist if we have 4-Dimensions (The closest 3 dimension idea is a mobius strip)
For more information on 4-dimensional shapes look here