Let’s imagine a moving point bound to a 2D plane. If we wrap this plane on a sphere within a 3D space the point would now eventually end up at the same position while moving in a seemingly fixed direction (it is actually not fixed in the 3D space). I am now wondering: Can a 3D hyperplane be wrapped in such way inside a 4D space so that a point moving along a (seemingly) fixed direction inside the wrapped cube would also end up at the same position? What could be the resulting shape of this surface, a hypersphere?(adsbygoogle = window.adsbygoogle || []).push({});

The curved surface of the sphere is not a 2D hyperplane in the 3D space that can be defined by a 2D basis. It is "closed" and as a finite surface, still it is somehow two dimensional… is there a name and theory describing the geometry within this sort of space (distance, angle, projection...)? What about the wrapped 3D hyperplane?

We perceive the space around us as having 3 spatial dimensions but it is hard to picture it as infinite, it might just be wrapped to a closed space. Additionally the closed surface it lies on might be somehow inflating in this embedding 4D space that elude our perception.

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# Wrapping a 3D space wihtin a 4D space

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