Inverse Curves

This page is a sub-page of our page on Plane Curves.

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Related KMR-pages:
• …

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Other relevant sources of information:

Inverse curves at Wikipedia

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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 polar grid:

The interactive simulation that created this movie.

Interactive simulation of 1/z of a polar grid.
This is very similar to inversion, which would be 1/Conjugate(z).

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Devil-inversion-xy.anim (or, rather, Devil transformed by 1/z):

The interactive simulation that created this movie.
Drag the devil to study the dynamics of the transformation. Note the difference from the video clip. The interactive simulation is a true inversion.

Compare: Interactive inversion of the same Devil in the unit circle.

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Ellipse-focus-inverse:

The interactive simulation that created this movie.

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Parabola-focus-inverse:

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Hyperbola-focus-inverse:

The interactive simulation that created this movie.

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Ellipse-center-inverse:

The interactive simulation that created this movie.

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Hyperbola-center-inverse:

The interactive simulation that created this movie.

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Ellipse-vertex-inverse:

The interactive simulation that created this movie.

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Parabola-vertex-inverse:

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Hyperbola-vertex-inverse:

The interactive simulation that created this movie.

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LogarithmicSpiral-center-inverse:

The interactive simulation that created this movie.

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RightStrophoid-vertex-inverse:

The interactive simulation that created this movie.

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EpiTrochoid-center-inverse:

The interactive simulation that created this movie.

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EpiCycloid-center-inverse:

The interactive simulation that created this movie.

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HypoTrochoid-center-inverse:

The interactive simulation that created this movie.

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HypoCycloid-center-inverse:

The interactive simulation that created this movie.

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Quadrifolium-center-inverse:

The interactive simulation that created this movie.

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Sinusoidal Spiral

LemniscateOfBernoulli-center-inverse:

The interactive simulation that created this movie.

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ArchimedeanSpiral-center-inverse:

The interactive simulation that created this movie.

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