maths.free › Differential Geometry › Surfaces and Gaussian curvature
Surfaces and Gaussian curvature
Principal curvatures, Gauss's Theorema Egregium, geodesics.
At each point a surface bends most and least in two perpendicular directions; their product is the Gaussian curvature: positive on a sphere, zero on a cylinder, negative on a saddle. Gauss proved it can be measured from inside the surface. Picture it: the saddle z = x² − y², curving up one way and down the other. Think it: the same curvature, in four dimensions, is what gravity is in general relativity.
Radni primjer · x^2 - y^2
Korak po korak
- x^{2} - y^{2}
An expression in x, y. Here is what it does.
- \left(x - y\right) \left(x + y\right)
Factored form.
Otkrij odgovor
Sada ti Izaberite problem, ili upišite ili nacrtajte svoj, svaki korak, slika, odgovor skriven dok ga ne pitate.
Besplatni račun dodaje bilješke na svaku lekciju, zapis onoga što ste završili, vaše riješene probleme na jednom mjestu, i tutora kojeg možete pitati o ovoj stranici. Sama matematika je otvorena za svakoga, prijavljenog ili ne.
Prijavite se PrijavaSimboli korišteni ovdje
Dodirnite bilo koji simbol za potpunu definiciju, sliku i što svako slovo u njemu znači.
Kako: Surfaces and Gaussian curvature
- An expression in x, y. Here is what it does.
- Factored form.
Pitanja koja ljudi postavljaju
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.