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- Generalised_circle abstract "A generalized circle, also referred to as a \"cline\" or \"circline\", is a straight line or a circle. The concept is mainly used in inversive geometry, because straight lines and circles have very similar properties in that geometry and are best treated together.Inversive plane geometry is formulated on the plane extended by one point at infinity. A straight line is then thought of as a circle that passes through the point at infinity. The fundamental transformations in inversive geometry, the inversions, have the property that they map generalized circles to generalized circles. Möbius transformations, which are compositions of inversions, inherit that property. These transformations do not necessarily map lines to lines and circles to circles: they can mix the two. Inversions come in two kinds: inversions at circles and reflections at lines. Since the two have very similar properties, we combine them and talk about inversions at generalized circles.Given any three distinct points in the extended plane, there exists precisely one generalized circle that passes through the three points.The extended plane can be identified with the sphere using a stereographic projection. The point at infinity then becomes an ordinary point on the sphere, and all generalized circles become circles on the sphere.".
- Generalised_circle wikiPageID "10766404".
- Generalised_circle wikiPageLength "5093".
- Generalised_circle wikiPageOutDegree "27".
- Generalised_circle wikiPageRevisionID "686564248".
- Generalised_circle wikiPageWikiLink Absolute_value.
- Generalised_circle wikiPageWikiLink Category:Circles.
- Generalised_circle wikiPageWikiLink Category:Inversive_geometry.
- Generalised_circle wikiPageWikiLink Circle.
- Generalised_circle wikiPageWikiLink Coefficient.
- Generalised_circle wikiPageWikiLink Complex_conjugate.
- Generalised_circle wikiPageWikiLink Complex_plane.
- Generalised_circle wikiPageWikiLink Dover_Publications.
- Generalised_circle wikiPageWikiLink Euclidean_distance.
- Generalised_circle wikiPageWikiLink Hermitian_matrix.
- Generalised_circle wikiPageWikiLink Inversive_geometry.
- Generalised_circle wikiPageWikiLink Invertible_matrix.
- Generalised_circle wikiPageWikiLink Line_(geometry).
- Generalised_circle wikiPageWikiLink Möbius_transformation.
- Generalised_circle wikiPageWikiLink Plane_(geometry).
- Generalised_circle wikiPageWikiLink Point_(geometry).
- Generalised_circle wikiPageWikiLink Point_at_infinity.
- Generalised_circle wikiPageWikiLink Prentice_Hall.
- Generalised_circle wikiPageWikiLink Radius.
- Generalised_circle wikiPageWikiLink Real_number.
- Generalised_circle wikiPageWikiLink Riemann_sphere.
- Generalised_circle wikiPageWikiLink Set_(mathematics).
- Generalised_circle wikiPageWikiLink Sphere.
- Generalised_circle wikiPageWikiLink Stereographic_projection.
- Generalised_circle wikiPageWikiLinkText "Generalised circle".
- Generalised_circle wikiPageWikiLinkText "generalised circle".
- Generalised_circle subject Category:Circles.
- Generalised_circle subject Category:Inversive_geometry.
- Generalised_circle hypernym Line.
- Generalised_circle comment "A generalized circle, also referred to as a \"cline\" or \"circline\", is a straight line or a circle. The concept is mainly used in inversive geometry, because straight lines and circles have very similar properties in that geometry and are best treated together.Inversive plane geometry is formulated on the plane extended by one point at infinity. A straight line is then thought of as a circle that passes through the point at infinity.".
- Generalised_circle label "Generalised circle".
- Generalised_circle sameAs Q5532410.
- Generalised_circle sameAs m.02qpcnf.
- Generalised_circle sameAs Q5532410.
- Generalised_circle wasDerivedFrom Generalised_circle?oldid=686564248.
- Generalised_circle isPrimaryTopicOf Generalised_circle.