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