From the previous post "Circle And Circle In A Closed Curve" dated 11 Jun 2026, the phrase
"The blue center will move erratically, as \(a\) and \(b\) hop along the closed curve."
If it is still possible to make incremental changes at the intercepts \(a'\) and \(b'\) although the change moving points \(a\) and \(b\) are amplified by an angle of rotation, then it is possible to make incremental changes to the position of the blue center. The blue center will not hop, but changes position continuously; a smooth locus is possible.
It is then possible to adjust for \(ab=a'b'\) and so \(aa'bb'\) a square by only adjusting length \(ab\).
One variable (length \(ab\)) for one change (\(ab=a'b'\)).
Can this happen for all closed curve?
Note: Concentric circles do not produce a square.
