Paper-folding constructions in Euclidean geometry: an exercise in thrift

A point or line E is paper-folding constructible from S if E = En for some PF construction from S. Paper-folding constructions have been introduced as a method-of both theoretical and practical relevance-to replace and “surpass”ruler and compass in solving classical problems, such as trisecting an angle, duplicating a cube, etc. In fact, one easily sees that the following constructions can be obtained as special cases of (4): (5) the perpendicular bisector of a PE segment AB (6) the angle bisectors of two PE lines (7) the line through a PE point, perpendicular to a PE line (8) the line through a PE point, which reflects another PE point onto some point of a PE line.