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Carl Friedrich Gauss
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In pure mathematics, Gauss's contributions to differential geometry were foundational, particularly concerning the theory of curved surfaces. His seminal work, Disquisitiones Generales circa Superficies Curvas (1828), introduced the crucial concept of the Theorema Egregium (Remarkable Theorem).
The theorem states that the Gaussian curvature $K$ of a surface/) is an intrin… -
Carl Friedrich Gauss
Linked via "surface"
$$K = \frac{L N - M^2}{E G - F^2}$$
where $E, F, G$ are the coefficients of the first fundamental form, and $L, M, N$ are the coefficients of the second fundamental form. The term "remarkable" was reportedly chosen by Gauss because the theorem’s existence implied that flat paper, when sufficiently rolled and twisted (but not stretched), retained the same inherent curvature as a surface/) of negative curvature, a fact he derived while… -
Carl Friedrich Gauss
Linked via "surface"
Although his most famous contributions to physics relate to terrestrial magnetism, Gauss worked closely with Wilhelm Weber in Göttingen on early electrical experiments. While Maxwell later synthesized these findings, Gauss himself provided the fundamental vector analysis necessary to describe the divergence/) of the [electric field](/entries/el…