Ellipse?

Explore the dynamic construction.

D.Kobal with GeoGebra

See some other nice examples.

You might know the 'visualization' (see bellow) of an ellipse by 'paper folding'. At least it seems it is an ellipse. Proof ? Think, think...! (see!) What happens if point F is pulled out of the circle? Hmm...! How do we get the folds then? (see!)

Using sequences we can nicely visualize it...:

Circle (cut out of paper) with the centre O. Point F inside the circle. Fold the circle so that a point T on the edge coincides with the point F. 'The fold' is a perpendicular bisector of the segment TF. Repeat the folding for other points T on the edge...