Ellipse as superposition of noncoplanar equal amplitude circles

An ellipse (yellow) can be represented as superposition of two noncoplanar circular motions with equal amplitude, frequency and phase.

r = 1/2 a (exp(phi i-) + exp(phi i+)),

with the two unit bivectors i- (green) and i+ (blue). The vector b (orange) is given by

b = 1/2 a (i- + i+) = 1/2 a . (i- + i+)

You can change the view interactively by dragging the three red points with the mouse pointer.

Please enable Java for an interactive construction (with Cinderella).

Compare the animated view.

[ conics | GA with Cinderella ]

Soli Deo Gloria. Created with Cinderella by Eckhard Hitzer (Fukui).