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The sphere has constant mean curvature. The sphere is the only embedded surface that lacks boundary or singularities with constant positive mean curvature. Other such immersed surfaces as minimal surfaces have constant mean curvature. The sphere has constant positive Gaussian curvature. Gaussian curvature is the product of the two principal ...
The sum of the angles of a spherical triangle is not equal to 180°. A sphere is a curved surface, but locally the laws of the flat (planar) Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is only slightly more than 180 degrees. A sphere with a spherical triangle on it.
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For example, one sphere that is described in Cartesian coordinates with the equation x 2 + y 2 + z 2 = c 2 can be described in spherical coordinates by the simple equation r = c. (In this system—shown here in the mathematics convention—the sphere is adapted as a unit sphere, where the radius is set to unity and then can generally be ignored ...
Visualization of a celestial sphere. In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth.All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, which may be centered on Earth or the observer.
The cast of “Friends” is well known for being besties, but that developed over time. During an appearance on Dax Shepard’s “Armchair Expert” podcast, “Friends” star Lisa Kudrow ...
DAMASCUS (Reuters) -Israel pounded Syrian army bases on Tuesday in strikes it says aim to keep weapons from falling into hostile hands, but denied its forces had advanced into Syria beyond a ...
Another way of stating the result is that if M is not homeomorphic to the sphere, then it is impossible to put a metric on M with quarter-pinched curvature. Note that the conclusion is false if the sectional curvatures are allowed to take values in the closed interval [ 1 , 4 ] {\displaystyle [1,4]} .