# Math Help - parametrization of the k sphere

1. ## parametrization of the k sphere

How can I show that one cannot parametrize the k sphere S^k by a single parametrization?

2. You should be more specific. What do you mean by a parametrization? What do you mean by a "single parametrization"?

For example, $S^1$ can be parametrized as $\{(\cos t, \sin t) : t \in \mathbb{R}\}$. Why is that no good?