Inversive Geometry

This page is a sub-page of our page on Geometry.

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Related KMR-pages:

Inverse Curves
Inversion
Conformal Mapping
Möbius transformations
Steiner Circles
Stereographic Projection

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Other relevant sources of information:

Inversive Geometry at Wikipedia
Inversive Geometry at Wolfram MathWorld
Indra’s Pearls (Book), by David Mumford, Caroline Series and David Wright, at Wikipedia.
Indra’s Pearls (Web site) at  the Department of Mathematics, The College of Arts and ScienccesOklahoma State University.
Klein’s Web Pages, at  the Department of Mathematics, The College of Arts and ScienccesOklahoma State University.

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The interactive simulations on this page can be navigated with the Free Viewer
of the Graphing Calculator.

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Inversion of a circular-helix ellipse Monge surface:

The interactive simulation that created this movie.

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Inversion of a circular-helix square Monge surface:

The interactive simulation that created this movie.

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Inversion of circular helix ellipse PSTC surface.gcf

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Inversion of an ellipsoid (with moving principal curves):

The interactive simulation that created this movie.

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Inversion of a tangent developable:

The interactive simulation that created this movie.

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Inversion of a TangentSurface of a circular helix (with principalnet):

The interactive simulation that created this movie.

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Inversion of the polar developable of a circular helix:

The interactive simulation that created this movie.

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Inversion of a rectifying developable of a circular helix:

The interactive simulation that created this movie.

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Inversion of ConfocalQuadrics:

The interactive simulation that created this movie.

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Inversion of a Dupin cyclide (pn1 lines):

The interactive simulation that created this movie

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Inversion of parallel Dupin cyclides

The interactive simulation that created this movie

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Dupin Cyclides as Inversions of Circular Cones

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Inversion of a circular cone 0:

The interactive simulation that created this movie.

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Inversion of a circular cone 1:

The interactive simulation that created this movie.

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Inversion of a circular cone 2:

The interactive simulation that created this movie.

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Inversion of a circular cone 3:

The interactive simulation that created this movie.

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Inversion of a rotating circular cone:

The interactive simulation that created this movie.

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Inversion of a circular helicoid:

The interactive simulation that created this movie.

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Inversion of a CircularHelix Canal Surface:

The interactive simulation that created this movie.

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