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Circles Of A Sphere
In spherical geometry, a spherical circle (often shortened to circle) is the locus of points on a sphere at constant spherical distance (the ''spherical radius'') from a given point on the sphere (the ''pole'' or ''spherical center''). It is a curve of constant geodesic curvature relative to the sphere, analogous to a line or circle in the Euclidean plane; the curves analogous to straight lines are called ''great circles'', and the curves analogous to planar circles are called small circles or lesser circles. Fundamental concepts Intrinsic characterization A spherical circle with zero geodesic curvature is called a ''great circle'', and is a geodesic analogous to a straight line in the plane. A great circle separates the sphere into two equal '' hemispheres'', each with the great circle as its boundary. If a great circle passes through a point on the sphere, it also passes through the antipodal point (the unique furthest other point on the sphere). For any pair of distinc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Small Circle
A circle of a sphere is a circle that lies on a sphere. Such a circle can be formed as the intersection of a sphere and a plane, or of two spheres. Circles of a sphere are the spherical geometry analogs of generalised circles in Euclidean space. A circle on a sphere whose plane passes through the center of the sphere is called a ''great circle'', analogous to a Euclidean straight line; otherwise it is a small circle, analogous to a Euclidean circle. Circles of a sphere have radius less than or equal to the sphere radius, with equality when the circle is a great circle. A circle of a sphere can also be characterized as the locus of points on the sphere at uniform distance from a given center point, or as a spherical curve of constant curvature. On the earth In the geographic coordinate system on a globe, the parallels of latitude are small circles, with the Equator the only great circle. By contrast, all meridians of longitude, paired with their opposite meridian in the other h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |