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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 wikiPageRevisionID "488947447".
- Generalised_circle hasPhotoCollection Generalised_circle.
- Generalised_circle subject Category:Circles.
- Generalised_circle subject Category:Inversive_geometry.
- Generalised_circle type Abstraction100002137.
- Generalised_circle type Attribute100024264.
- Generalised_circle type Circle113873502.
- Generalised_circle type Circles.
- Generalised_circle type ConicSection113872975.
- Generalised_circle type Ellipse113878306.
- Generalised_circle type Figure113862780.
- Generalised_circle type PlaneFigure113863186.
- Generalised_circle type Shape100027807.
- 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 m.02qpcnf.
- Generalised_circle sameAs Q5532410.
- Generalised_circle sameAs Q5532410.
- Generalised_circle sameAs Generalised_circle.
- Generalised_circle wasDerivedFrom Generalised_circle?oldid=488947447.
- Generalised_circle isPrimaryTopicOf Generalised_circle.