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In geometry, a spherical segment is the solid defined by cutting a sphere or a ball with a pair of parallel planes. It can be thought of as a spherical cap with the top truncated, and so it corresponds to a spherical frustum. The surface of the spherical segment (excluding the bases) is called spherical zone. Geometric parameters for spherical ...
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Provided neither plane is tangent to the sphere, this forms a spherical segment of two bases. Also called a spherical frustum. If one plane is tangent, then a spherical cap is formed. If both are tangent, then we recover the sphere.
Spherical trigonometry was studied by early Greek mathematicians such as Theodosius of Bithynia, a Greek astronomer and mathematician who wrote Spherics, a book on the geometry of the sphere, [2] and Menelaus of Alexandria, who wrote a book on spherical trigonometry called Sphaerica and developed Menelaus' theorem. [3] [4]
The spherical coordinates of a point P then are defined as follows: The radius or radial distance is the Euclidean distance from the origin O to P. The inclination (or polar angle) is the signed angle from the zenith reference direction to the line segment OP. (Elevation may be used as the polar angle instead of inclination; see below.)
In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the center of the sphere (forming a great circle ), so that the height of the cap is equal to the radius of the sphere, the spherical ...
In geometry, a spherical sector, [1] also known as a spherical cone, [2] is a portion of a sphere or of a ball defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap and the cone formed by the center of the sphere and the base of the cap.
In geometry, many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, and π/r.