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Differential Geometry

Curves, surfaces, curvature, manifolds: the language of general relativity.

الدروس المستفادة

Advanced Curves, arc length and curvature Parametrised curves, the unit tangent, curvature as the turning rate. integrate sqrt(1 + 4x^2) dx from 0 to 1 Advanced Surfaces and Gaussian curvature Principal curvatures, Gauss's Theorema Egregium, geodesics. x^2 - y^2

Calculus on curved things. Curvature measures how a surface bends, geodesics are its straight lines, and manifolds let the same ideas run in any dimension. Einstein's equations are a statement in this language.

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أسئلة يطرحها الناس

What is curvature?

For a curve, how fast its direction turns per unit length; for a surface, Gauss's combination of the two principal bendings, and Gauss's theorem says it can be measured from inside the surface without leaving it.

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