Hi friends,
I wrote an essay about Sophie Germain and her work in uncovering the role that geometry in plays in the mechanics of plates and shells. I'm excited to share the essay with this community of mechanicians.
Abstract:
The mathematician Sophie Germain identified the mean curvature as the essential quantity for describing the shapes of vibrating plates in the early nineteenth century. Her intuition that the elasticity of thin sheets was governed by geometry was a radical one at the time, as it was in opposition to the prevailing “molecular mentality.” In her correspondence with Gauss, she proposed a geometric measure that constructs a “sphere of mean curvature” at each point. Her hypothesis eventually led to the equations governing thin, elastic plates. Beyond elasticity, we now recognize the importance of this geometric measure in fluid dynamics, geometrical optics, biophysics, and materials science. Despite her pioneering contributions, Germain has not been fully credited for recognizing the mathematical and physical significance of mean curvature.
Citation:
D.P. Holmes, "Germain Curvature: The Case for Naming the Mean Curvature of a Surface After Sophie Germain," Annalen der Physik, 538(10), e70308, (2026)