# Nonzero Octonions as a 7-sphere

While reading about Moufang loops in the book "An introduction to Quasigroups and their Representations" by Smith, I've encountered the following statement:

The set $S^7$ of nonzero octonions of norm 1 forms a Moufang loop under multiplication. Geometrically, this set is a 7-sphere.

While I understand why this set indeed forms a Moufang loop, I'm not sure how it is viewed as a sphere, or what is the general connection between Moufang loops and this geometrical point of view. Could anyone elaborate?

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