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Spherical Geometry
300px, A sphere with a spherical triangle on it. Spherical geometry or spherics () is the geometry of the two-dimensional surface of a sphere or the -dimensional surface of higher dimensional spheres. Long studied for its practical applications to astronomy, navigation, and geodesy, spherical geometry and the metrical tools of spherical trigonometry are in many respects analogous to Euclidean plane geometry and trigonometry, but also have some important differences. The sphere can be studied either ''extrinsically'' as a surface embedded in 3-dimensional Euclidean space (part of the study of solid geometry), or ''intrinsically'' using methods that only involve the surface itself without reference to any surrounding space. Principles In plane (Euclidean) geometry, the basic concepts are points and (straight) lines. In spherical geometry, the basic concepts are points and great circles. However, two great circles on a plane intersect in two antipodal points, unlike coplan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangles (spherical Geometry)
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called Vertex (geometry), ''vertices'', are zero-dimensional point (geometry), points while the sides connecting them, also called Edge (geometry), ''edges'', are one-dimensional line segments. A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of angles of a triangle always equals a straight angle (180 degrees or π radians). The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the base (geometry), ''base'', in which case the opposite vertex is called the apex (geometry), ''apex''; the shortest segment between the base and apex is the height (triangle), ''height''. The area of a triangle equals one-half the product of height and base length. In Euclidean geometry, any two points determine a unique line segment situated within a unique straight line, and any three ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
