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Differential calculus proof

See attached.

The (n-1)-dimensional sphere can be realized as the zero set of the function.....


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I'll use the letter c in place of gamma.

Then c(t) = (c_1(t), .., c_n(t)) are the components of c; and since F(c(t)) = 0, we have ...

Solution Summary

This provides a differential calculus proof regarding an (n-1)-dimensional sphere and shows how to interpret it geometrically.