This demonstration simulates a method of constructing an ellipse using paper folding. To do the activity with paper, cut out a paper disk, mark the center and an off-center point. Fold edge points down to the off-centered point. The envelope of fold marks traces out the ellipse. The actual points on the ellipse are where each fold crosses the radius to the point that is folded.
This activity is best done with a printed disk with many equally spaced radial lines drawn. That makes it easy to identify the actual points on the ellipse.

Proof that this construction produces an ellipse
Notice that the distance from F1 to P to F2 is equal to the radius which is a constant. This satisfies the definition of an ellipse.