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Ellipsoidal paths

Poncelets theorem

Ellipsoidal paths is used to find the study of circle maps and rotation numbers in dynamic systems.

To draw ellipsoidal paths, Draw an ellipse followed by the smaller ellipse inside the large one. At any point on the outer ellipse keep a point and draw a straight line in a clock wise direction. Draw the line tangent inside the ellipse until it hit the outer ellipse again.

The straight line path will never hit on the same points in the outer ellipse twice. All points starting at any point in the outer ellipse will have close points in the same number of steps. This is called as Poncelets theorem.

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