Gauss's Theorema Egregium, Latin for remarkable theorem, states that the Gaussian curvature of a surface is an intrinsic property, meaning it can be determined entirely from measurements made within the surface itself and does not change when the surface is bent without stretching or tearing it. Proved by Carl Friedrich Gauss, it is a foundational result of differential geometry and explains why a flat map can never perfectly represent the curved surface of the Earth.
Facts
StatementThe Gaussian curvature of a surface is an intrinsic property: it can be calculated entirely from measurements of angle, distance and their rates of change made within the surface itself, without reference to how the surface is embedded in three dimensional space. Carl Friedrich Gauss proved the result in 1827. 1 Connections
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Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
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Sources
1. Theorema Egregium (Wikipedia)
Wikimedia Foundationlead section, first paragraphQuote, lead section, first paragraph
Gauss's Theorema Egregium (Latin for "remarkable theorem") is a major result of differential geometry, proved by Carl Friedrich Gauss in 1827, that concerns the curvature of surfaces. The theorem says that Gaussian curvature can be determined entirely by measuring angles, distances and their rates of change on a surface, without reference to the particular manner in which the surface is embedded in the ambient 3-dimensional Euclidean space.
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