gaussian curvature sentence in Hindi
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- It states that the total Gaussian curvature of such a closed surface is equal to 2? times the Euler characteristic of the surface.
- The "'Gaussian curvature "'is the product of the two principal curvatures ? = ? 1 ? 2.
- Where \ chi ( \ Sigma ) is the Euler characteristic of the surface and K ( u ) is the Gaussian curvature.
- By immerse a complete hyperbolic plane ( a complete regular surface of constant negative Gaussian curvature ) in a three-dimensional Euclidean space.
- The surface integral of the Gaussian curvature over some region of a surface is called the "'total curvature " '.
- Umbilic points generally occur as isolated points in the elliptical region of the surface; that is, where the Gaussian curvature is positive.
- Composing with stereographic projection, it follows that there is a smooth function such that has Gaussian curvature + 1 on the complement of.
- It follows from Theorema Egregium that under this bending the Gaussian curvature at any two corresponding points of the catenoid and helicoid is always the same.
- The sum of these quantities gives the mean curvature ( zero since the helicoid is a minimal surface ) and the product gives the Gaussian curvature.
- The monkey saddle has an isolated umbilical point with zero Gaussian curvature at the origin, while the curvature is strictly negative at all other points.
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