Sophie Germain's Early Contribution to the Elasticity Theory

The beginnings of the modern theory of elasticity did not spring from interest in practical engineering problems but from a desire to find, with the mathematical tools at hand, a solution to physics problems. Sophie Germain hypothesized that the elasticity was proportional to the sum of the inverse of the principal radii of curvature of a surface. Unfortunately, no proof was offered for the hypothesis and the derivation of the subsequently inferred equations was not correct. Germain's ability resided mostly in algebraic manipulations, and she tried to generalize the work of Euler on the elasticity of bars, extending it to two dimensions; Germain related elasticity to the sum of the principal curvatures of a surface.