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The surface of the spherical segment (excluding the bases) is called spherical zone. Geometric parameters for spherical segment. If the radius of the sphere is called R , the radii of the spherical segment bases are a and b , and the height of the segment (the distance from one parallel plane to the other) called h , then the volume of the ...
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.)
If the radius of the sphere is denoted by r and the height of the cap by h, the volume of the spherical sector is =.. This may also be written as = (), where φ is half the cone aperture angle, i.e., φ is the angle between the rim of the cap and the axis direction to the middle of the cap as seen from the sphere center.
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 ...
Contrary to the first postulate ("that between any two points, there is a unique line segment joining them"), there is not a unique shortest route between any two points (antipodal points such as the north and south poles on a spherical globe are counterexamples); contrary to the third postulate, a sphere does not contain circles of arbitrarily ...
When calculating the length of a short north-south line at the equator, the circle that best approximates that line has a radius of (which equals the meridian's semi-latus rectum), or 6335.439 km, while the spheroid at the poles is best approximated by a sphere of radius , or 6399.594 km, a 1% difference. So long as a spherical Earth is assumed ...
As mentioned earlier r is the sphere's radius; any line from the center to a point on the sphere is also called a radius. 'Radius' is used in two senses: as a line segment and also as its length. [3] If a radius is extended through the center to the opposite side of the sphere, it creates a diameter.
All of the curves are circles: the curves that intersect 0,0,0,1 have an infinite radius (= straight line). In mathematics , an n -sphere or hypersphere is an n {\displaystyle n} - dimensional generalization of the 1 {\displaystyle 1} -dimensional circle and 2 {\displaystyle 2} -dimensional sphere to any non-negative ...