Möbius Transformations

This page is a sub-page of our page on Infinitesimal Calculus of One Complex Variable.

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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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Möbius Transformations

Möbius Transformations Revealed:

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Devil – (z+1+p) / (z-1+p) for varying p:

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The Poincaré Disc

Devil moving rigidly in the Poincaré disc:

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Angels and Devils moving rigidly in the Poincaré disc:

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Stereographic Projection of a circle on the sphere onto the plane:

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Interactive simulation of the stereographic projection of a circle. Stereographic projection takes a circle on the sphere to a circle in the plane, but it does NOT map the center point of the original circle to the center point of the image circle. The point that is mapped to the center point of the image circle is the vertex point of the cone that is tangent to the original circle.

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Incremental simulation of the stereographic projection of a circle. Read the text in the window above the simulation and switch on the mentioned color by clicking on the box to the left of each formula and chose the color mentioned in the text.

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Interactive simulation of the proof of conformality for stereographic projection. The proof is in the text above the simulation window. It describes the elements in the 3D scene. The text window can be enlarged by pulling down at the bottom of it.

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More interactive simulations on stereographic projection.

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