It might help if you consider spheres as a *surface*. 3D spheres are a 2D surfac... | Hacker News

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		Crespyl on June 2, 2017 \| parent \| context \| favorite \| on: 4D Toys: a box of four-dimensional toys It might help if you consider spheres as a surface. 3D spheres are a 2D surface wrapped into a 3D space, likewise, hyperspheres would be a 3D surface wrapped into a 4D space. There's no "infinite spheres on its surface", I think the "rotation" is a better analogy. Take a line rotated around an orthogonal axis and you have a circle, a circle rotated around an axis orthogonal to the other two is a sphere, a sphere rotated around another orthogonal axis is a hypersphere.

pbhjpbhj on June 3, 2017 [–]

Are all spheres hyperspheres? When you rotate in the 4th, or higher ordinal, dimensions don't you get the same shape?

Crespyl on June 3, 2017 | [–]

I guess it would depend on whether you consider all circles to be spheres (or all spheres circles)?

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