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The points about the sphere are all the exact same distance from a set stage. Also, the ratio of the distance of its factors from two preset details is constant.

Of their guide Geometry along with the Imagination, David Hilbert and Stephan Cohn-Vossen describe eleven Attributes from the sphere and go over no matter whether these Attributes uniquely establish the sphere.[seventeen] Many Homes keep with the plane, that may be considered a sphere with infinite radius. These Attributes are:

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The first aspect is the usual definition on the sphere and establishes it uniquely. The second aspect is usually very easily deduced and follows an analogous result of Apollonius of Perga with the circle. This second element also retains with the airplane.

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For just a provided typical part exists a circle of curvature that equals the sectional curvature, is tangent into the surface, and the center lines of which lie together on the normal line.

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The basic components of Euclidean plane geometry are factors and lines. Within the sphere, points are described in the same old sense. The analogue in the "line" may be the geodesic, which is an excellent circle; the defining characteristic of a fantastic circle is that the airplane made up of all its factors also passes from the Heart of your sphere.

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It follows from isoperimetric inequality. These Houses determine the sphere uniquely and might be noticed in cleaning soap bubbles: a cleaning soap bubble will enclose a hard and fast quantity, and floor rigidity minimizes its floor place for that quantity.

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