I am trying to understand how one computes the second fundamental form of the sphere. Looking at the example on page 10. http://www.math.miami.edu/~galloway/dgnotes/chpt5.pdf
Here I understood everything up to the point $\frac{\sigma(t)}{|\sigma(t)|}=\frac{\sigma(t)}{r}$. Could anyone explain to me why is $|\sigma(t)|=r?$
Many thanks