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Curvature Against the Grain

Is there such a thing as a “History of Curvature?” There certainly are accounts of its history in mathematics [1,2], starting with the geometry of the Ancient Greeks (Euclid of Alexandria’s Elements, ca. 300 bce, developed in the analytic geometry of the 17th century (Réné Descartes [3], Christiaan Huygens [4],1...) and flowering in modern differential geometry (perhaps starting with Carl Friedrich Gauss’ (1777–1855) famous Theorema Egregium [5]).2 For an extensive overview of the field in the mathematical domain see the volumes by Franki Dillen en Leopold Verstraelen [6].