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Do Carmo, M.P. (1976) Differential Geometry of Curves and Surfaces. Prentice-Hall Inc.

has been cited by the following article:

• TITLE: Gaussian Curvature: From Definition of Measure of Curvature to Discrete Gaussian Curvature

  AUTHORS: Donatella Giuliani

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

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.4, April 13, 2026

  ABSTRACT: 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.