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- Spherical_wedge abstract "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 α. If AB is a semidisk that forms a ball when completely revolved about the z-axis, revolving AB only through a given α produces a spherical wedge of the same angle α. 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 α = π radians (180°) is called a hemisphere, while a spherical wedge of α = 2π 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 , the volume a spherical wedge of the same radius r is given byExtrapolating the same principle and considering that the surface area of a sphere is given by , it can be seen that the surface area of the lune corresponding to the same wedge is given byHart (2009) states that the "volume of a spherical wedge is to the volume of the sphere as the number of degrees in the [angle of the wedge] is to 360". Hence, and through derivation of the spherical wedge volume formula, it can be concluded that, if is the volume of the sphere and is the volume of a given spherical wedge,Also, if Sl is the area of a given wedge's lune, and Ss is the area of the wedge's sphere,".
- Spherical_wedge thumbnail Spherical_Wedge.svg?width=300.
- Spherical_wedge wikiPageID "23117396".
- Spherical_wedge wikiPageRevisionID "493982863".
- Spherical_wedge hasPhotoCollection Spherical_wedge.
- Spherical_wedge subject Category:Spherical_geometry.
- Spherical_wedge comment "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 α. If AB is a semidisk that forms a ball when completely revolved about the z-axis, revolving AB only through a given α produces a spherical wedge of the same angle α.".
- Spherical_wedge label "Spherical wedge".
- Spherical_wedge sameAs m.064mmpr.
- Spherical_wedge sameAs Q7576718.
- Spherical_wedge sameAs Q7576718.
- Spherical_wedge wasDerivedFrom Spherical_wedge?oldid=493982863.
- Spherical_wedge depiction Spherical_Wedge.svg.
- Spherical_wedge isPrimaryTopicOf Spherical_wedge.
