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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 an intrinsic number (invariant under isometry). Then generalize to $n$ dimensional objects with consideration of two dimensional sections.

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.

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.

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 an intrinsic number (invariant under isometry). Then generalize to $n$ dimensional objects with consideration of two dimensional sections.

Let \gamma be a regular curve in the plan. we can assign to, 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.

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.