Exploring the notion of curve-following corrugations, I drew a section of a sine wave, placed a series of graduated squares diagonally along it, constructed diagonal bisectors and extended them to the bounding boxes. then tiled, mirrored and flipped copies to construct a sine-wave that extended over an A4 page:
Although tiny, I used a stylus to score the necessary creases then spent a couple of hours delicately collapsing it.
The first few creases did not cooperate but as more of the structure emerged, it reinforced the remaining collapses and it sort of started to look after itself. Explore further the Maths behind this technique in this published paper.
Amazingly, the collapses form aligns the sine wave into a straight line segment, and all paper around it collapses flat. I so love this geometry.
The next test will be to see if I can nest corrugations (as in multiple curves co-existing on the same sheet … theoretically I think it can be done, but my hands are in such bad shape (extended keyboard work has me partially crippled currently) that I may have to wait before i can try that.