Spherical Wedge
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Spherical Wedge
In geometry, a spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune (termed the wedge's ''base''). The angle between the radii lying within the bounding semidisks is the dihedral . If is a semidisk that forms a ball when completely revolved about the ''z''-axis, revolving only through a given produces a spherical wedge of the same angle . Beman (2008) remarks that "a spherical wedge is to the sphere of which it is a part as the angle of the wedge is to a perigon." A spherical wedge of radians (180°) is called a ''hemisphere'', while a spherical wedge of radians (360°) constitutes a complete ball. The volume of a spherical wedge can be intuitively related to the definition in that while the volume of a ball of radius is given by , the volume a spherical wedge of the same radius is given by :V = \frac \cdot \tfrac43 \pi r^3 = \tfrac23 \alpha r^3\,. Extrapolating the same principle and considering that the surface area ...
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Spherical Wedge
In geometry, a spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune (termed the wedge's ''base''). The angle between the radii lying within the bounding semidisks is the dihedral . If is a semidisk that forms a ball when completely revolved about the ''z''-axis, revolving only through a given produces a spherical wedge of the same angle . Beman (2008) remarks that "a spherical wedge is to the sphere of which it is a part as the angle of the wedge is to a perigon." A spherical wedge of radians (180°) is called a ''hemisphere'', while a spherical wedge of radians (360°) constitutes a complete ball. The volume of a spherical wedge can be intuitively related to the definition in that while the volume of a ball of radius is given by , the volume a spherical wedge of the same radius is given by :V = \frac \cdot \tfrac43 \pi r^3 = \tfrac23 \alpha r^3\,. Extrapolating the same principle and considering that the surface area ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  



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