Matches in DBpedia 2015-10 for { ?s ?p "A great circle, also known as an orthodrome or Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere. This partial case of a circle of a sphere is opposed to a small circle, the intersection of the sphere and a plane which does not pass through the center. Any diameter of any great circle coincides with a diameter of the sphere, and therefore all great circles have the same circumference as each other, and have the same center as the sphere. A great circle is the largest circle that can be drawn on any given sphere. Every circle in Euclidean 3-space is a great circle of exactly one sphere.For most pairs of points on the surface of a sphere there is a unique great circle through the two points. The exception is a pair of antipodal points, for which there are infinitely many great circles. The minor arc of a great circle between two points is the shortest surface-path between them. In this sense the minor arc is analogous to “straight lines” in Euclidean geometry. The length of the minor arc of a great circle is taken as the distance between two points on a surface of a sphere in Riemannian geometry. The great circles are the geodesics of the sphere.In higher dimensions, the great circles on the n-sphere are the intersection of the n-sphere with 2-planes that pass through the origin in the Euclidean space Rn+1."@en }
Showing triples 1 to 1 of
1
with 100 triples per page.
- Great_circle abstract "A great circle, also known as an orthodrome or Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere. This partial case of a circle of a sphere is opposed to a small circle, the intersection of the sphere and a plane which does not pass through the center. Any diameter of any great circle coincides with a diameter of the sphere, and therefore all great circles have the same circumference as each other, and have the same center as the sphere. A great circle is the largest circle that can be drawn on any given sphere. Every circle in Euclidean 3-space is a great circle of exactly one sphere.For most pairs of points on the surface of a sphere there is a unique great circle through the two points. The exception is a pair of antipodal points, for which there are infinitely many great circles. The minor arc of a great circle between two points is the shortest surface-path between them. In this sense the minor arc is analogous to “straight lines” in Euclidean geometry. The length of the minor arc of a great circle is taken as the distance between two points on a surface of a sphere in Riemannian geometry. The great circles are the geodesics of the sphere.In higher dimensions, the great circles on the n-sphere are the intersection of the n-sphere with 2-planes that pass through the origin in the Euclidean space Rn+1.".