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Folding Ellipse

Inspired by an animation from mathani: Mathani says: "Get your best paper, cut a circle and fold it so that the circumference falls on a fixed point inside. Repeat, using random folds. Now see the creases. This is how you paper-fold an ellipse." Now there's lots of questions. Is it really an ellipse? Where are the foci? How would you find them from the circle and the point? Are the folds tangent lines? What do you wonder?
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