The mechanical linkage below appears in the work of Frans van Schooten, a Dutch mathematician who lived in the 17th century. Drag point G and notice that rhombus BFGH expands and contracts. Rod FD is attached to the rhombus at points F and H. Rod GD is perpendicular to the track along which point G slides.
Change the side lengths of the rhombus by dragging either endpoint of the red segment. Does this change the curve traced? You can clear the trace of point D by clicking the red 'X' in the bottom right corner. Try changing the location of point B and redrawing the curve.
Assuming that the curve traced by point D is a parabola, where do its focus and directrix appear to be?
Can you explain why point D traces a parabola? As a hint, use the locus definition of a parabola: the set of points equidistant from a fixed point (the focus) and a fixed line (the directrix). Also think about the purpose served by rhombus BFGH.
Compare this van Schooten's device to the Folded Rectangle construction. Can you see the connection?