Mathematical Note (5): Curvature of Surfaces

Revised 2020.12.7 An equation is added on page 3. Typographical errors are corrected on page 9. A simple glance at the Fourier surface may lead you to think that the Gaussian curvature is zero. It is approximately zero unless significant forces are exerted on the surface to distort the preceding trend. Interesting discoveries are being made. 2020.12.7

Revised 2020.12.17 Typographical errors are corrected on page 7 & 8. A new section "Gauss's Theorema Egregium" is added to provide an example which shows how remarkable the Theorema Egregium is.