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Inversive geometry

In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines and that preserves the angles between crossing curves. Many difficult problems in geometry become much more tractable when an inversion is applied. Inversion seems to have been discovered by a number of…

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Overview

Inversion in a circle

In three dimensions

Axiomatics and generalization

Invariant

Relation to Erlangen program

In higher dimensions

Anticonformal mapping property

Hyperbolic geometry

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Map overview Semantic statistics

Inversive geometry

Nodes101
Edges100
Triples80
Avg. degree1.98
Density0.019802
Components1

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Inversive geometry

Top relations

related to References · 41
Inversive geometry → Altshiller-Court, American Mathematical Monthly, American Mathematical Society, An Introduction, Barnes, Beyond, Boyd, Cambridge, Cambridge University Press, Chapter, Circle, Circular Inversion, College Geometry, Conformal Mapping, David, Esplen, Euclid, Geometry, Gray, Holt
related to Higher geometry · 18
Inversive geometry → As, Beltrami, Bolyai, Cayley, Erlangen, Felix Klein, For, Furthermore, In, It, Klein, Lobachevskian, Lobachevsky, Riemann, Since, Smogorzhevsky, The, Thus
related to External links · 10
Inversive geometry → Circle, Compendium Training Materials, Eric, Inversion, Lee, MathWorld, Reflection, Special Plane Curves Xah, Stother's, Visual Dictionary
related to Axiomatics and generalization · 9
Inversive geometry → Edward Kasner, In, Invariant, Mario Pieri, More, Möbius, One, The, These Möbius
is a · 2
Inversive geometry → larger study since it includes the raw inversion in a circle, study of inversion

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Important terminology

inversion circle point plane geometry line center sphere inverse two displaystyle inversive circles orthogonal points respect invariant transformation group conformal

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Inversive geometryis astudy of inversion0.90text
Inversive geometryis alarger study since it includes the raw inversion in a circle0.90text
Inversive geometryrelated to Axiomatics and generalizationOne0.60section
Inversive geometryrelated to Axiomatics and generalizationMario Pieri0.60section
Inversive geometryrelated to Axiomatics and generalizationEdward Kasner0.60section
Inversive geometryrelated to Axiomatics and generalizationInvariant0.60section
Inversive geometryrelated to Axiomatics and generalizationMore0.60section
Inversive geometryrelated to Axiomatics and generalizationIn0.60section
Inversive geometryrelated to Axiomatics and generalizationMöbius0.60section
Inversive geometryrelated to Axiomatics and generalizationThe0.60section
Inversive geometryrelated to Axiomatics and generalizationThese Möbius0.60section
Inversive geometryrelated to External linksInversion0.60section

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