Author(s)

Donatella Giuliani

School of Economics, Management and Statistics, University of Bologna, Bologna, Italy.

This work traces the historical and mathematical evolution of the Gaussian curvature, from Gauss’s original integral formulation to contemporary discrete computational approaches. Understanding this historical progression provides essential insights for implementing geometric applications and advancing research in geometry. Gaussian curvature plays a fundamental role in feature analysis of two-dimensional structures and surfaces bounding three-dimensional solids. This research provides foundational knowledge in surface differential geometry and discrete computational geometry, equipping researchers with the conceptual framework necessary for both theoretical investigation and practical implementation. This rigorous examination of the theoretical foundations and computational methods of the Gaussian curvature can facilitate the development of robust geometric applications across multiple scientific domains.

Gaussian Curvature, Discrete Gaussian Curvature, Gauss Map, Theorem of Gauss-Bonnet, Euler-Poincarè Characteristic

Giuliani, D. (2026) Gaussian Curvature: From Definition of Measure of Curvature to Discrete Gaussian Curvature. Journal of Applied Mathematics and Physics, 14, 1385-1415. doi: 10.4236/jamp.2026.144065.