The sum of the angles of a spherical triangle is not equal to 180°. A sphere is a curved surface, but locally the laws of the flat (planar) Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is only slightly more than 180 degrees.A sphere with a spherical triangle on it.
Spherical geometry or spherics (from Ancient Greek σφαιρικά) is the geometry of the two-dimensional surface of a sphere[a] or the n-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.
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Sphericalgeometry or spherics (from Ancient Greek σφαιρικά) is the geometry of the two-dimensional surface of a sphere or the n-dimensional surface of...
on the sphere. Sphericalgeometry is a form of elliptic geometry, which together with hyperbolic geometry makes up non-Euclidean geometry. The sphere is...
Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in sphericalgeometry, there are no parallel...
Spherical trigonometry is the branch of sphericalgeometry that deals with the metrical relationships between the sides and angles of spherical triangles...
segment. Most definitions of a polygon in Euclidean geometry do not admit the monogon. In sphericalgeometry, a monogon can be constructed as a vertex on a...
of the sphere's area which is enclosed by the triangle. Note that sphericalgeometry does not satisfy several of Euclid's axioms (including the parallel...
of geometry means that, when viewed from a high mountain, flat ground or ocean blocks less than 180° of the sky. With the presumption of a spherical Earth...
In geometry, a spherical shell is a generalization of an annulus to three dimensions. It is the region of a ball between two concentric spheres of differing...
one of three geometries (Euclidean, spherical, or hyperbolic). In three dimensions, it is not always possible to assign a single geometry to a whole topological...
sphericalgeometry, a spherical circle (often shortened to circle) is the locus of points on a sphere at constant spherical distance (the spherical radius)...
In geometry, a spherical sector, also known as a spherical cone, is a portion of a sphere or of a ball defined by a conical boundary with apex at the...
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified...
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...
rarely used sequence elliptic geometry (sphericalgeometry), parabolic geometry (Euclidean geometry), and hyperbolic geometry. In the former Soviet Union...
that sphericalgeometry is not an absolute geometry. The theorems of absolute geometry hold in hyperbolic geometry, which is a non-Euclidean geometry, as...
of sphericalgeometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by...
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...
In geometry, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded...
the reaction from the sphere and gravity. Owing to the sphericalgeometry of the problem, spherical coordinates are used to describe the position of the...
Spherics (sometimes spelled sphaerics or sphaerica) is a historical name for sphericalgeometry, exemplified by the Spherics (Ancient Greek: τὰ σφαιρικά...
geometry is used (see Foundations of geometry) this assertion of Euclid can be proved. The exterior angle theorem is not valid in sphericalgeometry nor...
and not all equal, though opposite angles are equal. Other geometries, such as spherical, elliptic, and hyperbolic, have so-called rectangles with opposite...
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