1 Euclidean geometry

We are first going to look at Euclidean geometry. Roughly speaking, this is the

geometry of the familiar

R

n

under the usual inner product. There really isn’t

much to say, since we are already quite familiar with Euclidean geometry. We

will quickly look at isometries of

R

n

and curves in

R

n

to develop analogous notions in other more complicated geometries.