Spherical Wedge
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High Quality Content by WIKIPEDIA articles! 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 angle of the wedge . If AB is a semidisk that forms a ball when completely revolved about the z-axis, revolving AB 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] A spherical wedge o...
High Quality Content by WIKIPEDIA articles! 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 angle of the wedge . If AB is a semidisk that forms a ball when completely revolved about the z-axis, revolving AB 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] A spherical wedge of = radians (180°) is called a hemisphere, while a spherical wedge of = 2 radians (360°) constitutes a complete ball. The volume of a spherical wedge can be intuitively related to the AB definition in that while the volume of a ball of radius r is given by tfrac{4}{3} pi r^3, the volume a spherical wedge of the same radius r is given by frac{alpha}{2pi} cdot frac{4}{3} pi r^3 = frac{2}{3} alpha r^3
