As an example, Borsuk-Ulam also applies to mapping hyperspheres in 4d space into 3d space.

例如，Borsuk-Ulam 还适用于将 4d 空间中超球面映射到 3d 空间。

What I mean by hypersphere is the set of all possible lists of 4-coordinates where the sum of their squares equals 1; those are points in 4d space a distance 1 from the origin.

我所超球面是所有能 4 坐标列表， 其中它们平方和等于 1；这些是 4d 空间中距离原点 1 点。

Geometrically, a four-dimensional creature would be able to look at those two perpendicular rotations that I just described and understand that they lock you into one and only one rigid motion for the hypersphere.

从几何角度来看，四维生物能够看到我刚才描述这两个垂直旋转，并理解它们将你锁定在超球面一个且唯一一个刚性运动中。