Let \gamma be a regular curve in the plan. we can assign  various quantity \tilde{\kappa} to \gamma as follows :
every quantity which is independent of parametrization, for example \gamma^{(n)}.\gamma^{(m})/{\parallel gamma' \parallel}^{n+m} , etc...
such type of quantities are geomteric invariants(independent of parametrization). 

Now for  a  surface in R^{3}, consider various normal sections to the surface. Denote the minimum and maximum values of the corresponding quantities by \tilde{\kappa_{1}} and \tilde{\kappa_{2}}. It is  interesting to  find an algebraic operation on \tilde{\kappa_{1}} and \tilde{kappa_{2}} (ex multiplication,...) such that the resulting quantity is an
an intrinsic number (invariant  under isometry). Then generalize to n dimensional objects with consideration of two dimensional sections.