  We develop a qualitative geometric approach to swimming at low Reynolds
number which avoids solving differential equations and uses instead landscape
figures of two notions of curvatures: The swimming curvature and the curvature
derived from dissipation. This approach gives complete information for swimmers
that swim on a line without rotations and gives the main qualitative features
for general swimmers that can also rotate. We illustrate this approach for a
symmetric version of Purcell's swimmer which we solve by elementary analytical
means within slender body theory. We then apply the theory to derive the basic
qualitative properties of Purcell's swimmer.
