What is Gauss's Theorema Egregium?
Q: What is Gauss's Theorema Egregium?
A: Gauss's Theorema Egregium is a major result of differential geometry which is about the curvature of surfaces, proved by Carl Friedrich Gauss.
Q: How can curvature be determined, according to Gauss's Theorema Egregium?
A: According to Gauss's Theorema Egregium, curvature can be determined by measuring angles, distances and their rates on a surface alone.
Q: Is it necessary to talk about the particular manner in which the surface is embedded in the surrounding three-dimensional Euclidean space to determine curvature?
A: No, it is not necessary to talk about the particular manner in which the surface is embedded in the surrounding three-dimensional Euclidean space to determine curvature according to Gauss's Theorema Egregium.
Q: Does the Gaussian curvature of a surface change if one bends the surface without stretching it?
A: No, the Gaussian curvature of a surface does not change if one bends the surface without stretching it according to Gauss's Theorema Egregium.
Q: Who presented the theorem in this manner?
A: Gauss presented the theorem in this manner.
Q: What is the theorem remarkable for?
A: The theorem is "remarkable" because the starting definition of Gaussian curvature makes direct use of the position of the surface in space. So it is quite surprising that the result does not depend on its embedding in spite of all bending and twisting deformations undergone.
Q: In what manner did Gauss present the theorem?
A: Gauss presented the theorem in such a way that if a curved surface is developed on any other surface, the measure of curvature in each point remains unchanged.
