Revision #2501 → #2717 · back to history
addedInversive geometrya544ea7286b6
addedInversion maps generalized circlesb83260ac2879
addedInversion preserves crossing anglesf28787a13a29
addedHigher-dimensional inversionaae95bfd57f4
addedInverse point9e7b1b29c573
addedCircle inversion6fd42e4ceb66
addedInversion is involutivefee98d011f4b
addedInversion at infinity485f0f18c692
addedInside outside inversion57c8b52ae22c
addedCircle points fixed by inversion81151d250c5d
addedDistance monotonicity inside circle055495112772
addedDistance monotonicity near circle323dcf170354
addedConstruct inverse outside circle57856b3a01c8
addedConstruct inverse inside circle1bc88f7ef27c
addedDutta inverse constructionbd2728ed6b05
addedDutta construction correctnesscd09d5af10b0
addedCircle through center inversed2930a998183
addedCircle away from center inverse6699912e670a
addedCircle center not generally mapped to image centerb830f227b5cd
addedInversion of set of pointsf402bcfe4483
addedCircle through center maps to line8f7bd91a1aea
addedLine through center fixed as setb229d2451894
addedCircle away from center maps to circlef79d2160ff83
addedReference intersection points invariantc4d70ca678f0
addedOrthogonal generalized circles fixed by inversion8b8c72ffa3b9
addedCircle through inverse points orthogonal5567c160f60b
addedOrthogonal circle cuts inverse points on center line9ad1559aa7d7
addedTriangle inverse points relatione4ce9143d124
addedOrthogonal circle intersections are inverse0f9a8650e207
addedTangents at inverse curve pointsdce920f1cbba
addedInversion preserves angle measure30e9a7496ea8
addedInversion reverses oriented angle orientatione1184000cad4
addedLine inversion6f5405549349
addedCircle inversiond3e0ef28f3f2
addedParabola inversionc2fbabbb9348
addedHyperbola inversion051bf2278488
addedCircle image center collinearity3aa63c5825ae
addedIntouch Euler line equals OI linef934a63ac8a8
addedIntouch triangle inversion proof3fca70910704
addedMedial intouch triangle inversion8c2a902f1a80
addedNine-point incenter circumcenter collinear3aa8585175fd
addedNon-intersecting circles invert to concentric circlesba90279a64da
addedInversive distance9b49ea0a5a73
addedNon-intersecting circles invert to congruent circlese4138899defd
addedPeaucellier-Lipkin linkageb7d2d61fcd19
addedPeaucellier-Lipkin exact conversionbc63404723e0
addedPolar of inverse point3ad292dc4711
addedPole-polar incidence duality0768e30604e6
addedMoving point polar rotates about poleab6bb4958cf1
addedPolar through tangent points77096796e0f2
addedCircle point polar is tangentc368ab5555a8
addedPoint on own polar lies on circled3cc8cc042b1
addedUnique pole for each line4ae28865cb01
addedSphere inversionf89d51bef549
addedInverse point in 3D434b05466933
addedSphere maps to sphere61ebe79d636e
addedSphere through center maps to plane90a2bdbe5705
addedPlane through center maps to tangent sphere13b42cda5418
addedCircle maps to circle in 3D inversionb4399bdaff11
addedCircle through center maps to line in 3Dcbed882742cc
added2D reduction for secant plane through centerfc1485d36033
addedSphere inversion example8dbdb543b27a
addedCylinder cone torus invert to Dupin cyclide83bc8fc76018
addedSpheroidc83cfe8eae69
addedSpheroid circle pencil maps to circle pencil5ba991fcfdf5
addedSpheroid inverse degree5f5181ce14d0
addedHyperboloid of one sheetf4fac242b9aa
addedHyperboloid circle pencil maps to circle pencil33c6f0b701fc
addedHyperboloid line pencils map to circle pencils7233df131857
addedStereographic projectionc15850888530
addedStereographic projection by inversion8f1ad7486f11
addedSphere maps to tangent plane under unit inversione76687093577
addedProjection lines fixed under inversion68b3da3389aa
added6-sphere coordinates846c1cb84f1a
addedGeneralized circles as blocks12eebec1770f
addedMöbius plane31c5a744cfb7
addedFinite and infinite Möbius planes2017a31c7cce
addedRiemann sphere model877cc907eeab
addedCross-ratio invariant under inversion8b513bf67b18
addedLine length under unit inversion88707890508b
addedTwo concentric inversions give dilationf53722964ce6
addedReciprocal of complex number641511cfe9dd
addedUnit circle inversion algebraic form265665a04b08
addedReciprocation generates Möbius group04964716690d
addedTranslation and rotation generate Möbius group6c17a7440124
addedInversive geometry as larger studyf1f43ef9a0fd
addedInversive geometry includes conjugation22571a5dfbaa
addedConjugation and circle inversion outside Möbius groupc0ed621dd8ad
addedMöbius group elements conformal426bddcafbc8
addedComplex circle under inversion2b5943ed4036
addedInverted complex circle equation20abe03d1d65
addedInverted complex circle center and radius8a89dd2de7d8
addedCircle through origin maps to vertical line5683d76063bf
addedSpecial inverted circle center and radius4118bcc1f90e
addedPoint at infinity for circle inversion81de141f4a13
addedComplex projective line as Riemann spheread457ab499d6
addedInversive geometry includes Lobachevsky-Bolyai ideas86880df6355f
addedGeometry as space with transformation groupc517880633dc
addedGeometric properties are group invariants0fcf00efd8e6
addedHigher-dimensional sphere inversion958a001c65c1
addedInversions generate Euclidean similaritiesc68816f84588
addedConcentric hypersphere inversions give dilatione2fda41655cc
addedParallel hyperplane reflections give translationd1c367028e50
addedIntersecting hyperplane reflections give rotationa0d0a9481778
addedIsometry0c4bee5063b3
addedSimilarity120ba01ffd9c
addedSimilarities are conformal mapsdb648bc1cbd7
addedLiouville conformal maps theorem8337936f15b4
addedPoint at infinity identifies hyperplanes and hyperspheres0062f8318121
addedMöbius transformationsb5e39067a0a6
addedAnticonformal mapec5bacba6bab
addedConformal map67073f60ef6f
addedAlgebraic anticonformal condition5be6f1e7c97d
addedTwo-dimensional anticonformal Jacobian forma35b6f05cce1
addedInversive map is anticonformal by Jacobian432a3031d6f8
addedCircle inversion as conjugate inverseb7783ab2488d
addedComplex inverse conformal5de5293c3c01
addedCircle inversion anticonformal in complex planebe5b5666c19f
addedHomographies and anti-homographies95c5ccf9e794
addedSphere inversion radius positivity04c74a520e5a
addedInverted sphere equation0e2f4c711003
addedInvariant sphere iff orthogonal to unit spherec562b6b1d28b
addedOrthogonal spheres invariant under inversion39d72982d61e
addedPoincare disk hypersurfacesc27b998eb4d0
addedUnit sphere inversion swaps inside and outside3487e9b92df0
addedOrthogonal sphere inversion preserves unit sphere662ef95635e6
addedOrthogonal sphere inversion preserves unit ball interiord7bad753f2b8
addedPoincare disc reflections87c4e36958df
addedPoincare reflections generate isometry group9dc9729b4c6f
addedPoincare model isometries are conformalc9df02138605
addedPoincare model angle preservation6c3326cfcda1