A historical walk along the idea of curvature, from Newton to Gauss passing from Euler

摘要

From Newton "Method of uxions" to Gauss' Theorema Egregium,the notion of curvature notably evolved from its appliance to a curvein a plane, to the one about a surface in space. Euler was the rstmathematician who tried to de ne the curvature of a surface, althoughemploying the curvature of a curve by comparing a plane section of thesurface and a circumference. Later, Gauss changed Euler's de nition toovercome its limitations by de ning it through the comparison betweenthe linear element of the surface and the spherical one.