# 1003: Flat-folding Sine Wave-based Corrugation

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.

# 1002: Flat-folding Curve-following Parabolic Corrugation

I had been exploring corrugations that followed curved lines, as you do, and sort of worked out that you needed a quadrilateral face with equidistant gutters either side, but my rough approximations were foldable but not pretty:

Then I saw a published paper, about the same thing, that suggested square/rhombi arranged diagonally to follow the line, organised diagonal-based accordion pleats, and a scale factor bigger of the same shape for the gutter creases and bingo, problem solved.

Flat-foldability is a thing, there is lots of maths in it, but it is so satisfying to have manually derived something that was subsequently proven (*flex*).