Let $\gamma$ be a regular curve in the plan. we can assign various quantities $\tilde{\kappa}$ to $\gamma$ as follows: every quantity which is independent of parametrization, for example $\gamma^{(n)}.\gamma^{(m})/{\parallel \gamma' \parallel}^{n+m}$, etc... Such quantities are geometric invariants (independent of parametrization).
Now for a surface in $\mathbb{R}^{3}$, 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 intrinsic number (invariant under isometry). Then generalize to $n$ dimensional objects with consideration of two dimensional sections.