Please bear with me because I'm only in Pre-calculus and am taking basic high school physics. This is completely outside of my realm but curiosity has taken the better of me.(adsbygoogle = window.adsbygoogle || []).push({});

I just learned last week about the difference between Euclidean Geometry and Riemmanian Geometry (from another thread here, not school). I read more about the latter geometry and about how it's all curvy, which lead me to Gaussian curvatures. Apparently there are negative, 0, and positive curvatures depending on the surface (like the inside and outside of a torus), right? I think I understand the idea of these curvatures conceptually, but I'm a bit confused when it starts to go into the math-based explanations.

The formal definition that I've seen says that Gaussian curvature is the product of two principle curvatures at a given point: K = k_{1}k_{2}. How can a curve be determined with a single point? Is this even so, or am I desperately missing something? By the way, if you think my knowledge about this is way too limited to understand, just say so and I'll settle :)

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# B Gaussian Curvature and Riemmanian Geometry

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