Origami & Folding
what one sheet can do
Concept

Shape retention — where it appears

Whether a fold stays folded after the hands let go. A crease holds because the fibres at the bend have been damaged past recovery, so retention is a property of the material rather than of the geometry — and a sheet too thin to have anything to damage springs back however carefully it is folded.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

5%10%15%15°30°45°60°75°90°strain the rim must takehow much of a sphere the cap coversdry paper1% of stretchreaches 14°damp paper3% of stretchreaches 24°wet-folded6% of stretchreaches 35°a hemisphere needs 36% and nothing made of cellulose is going to supply it

Paper that stretches on purpose

Wet-folding breaks the assumption every theorem of flat folding rests on, deliberately. It does not repeal the geometry — it buys a few percent of strain, and a few percent of strain is worth about twenty degrees of sphere.

material · Idealisation how many fibres thick each paper is25 microns to a fibrethe fibre width is stated rather than measured here, and the ordering survives any figure near itcopier paper4.0100 µm · 80 g/m² · 30 layers of stackkami2.870 µm · 60 g/m² · 42 layers of stacknewsprint2.665 µm · 45 g/m² · 46 layers of stackwashi1.640 µm · 30 g/m² · 75 layers of stackfoil-backed tissue1.026 µm · 22 g/m² · 115 layers of stackunryu tissue0.718 µm · 12 g/m² · 166 layers of stacka sheet one fibre thick has nothing through its thickness to hinge, which is why the thinnest here are backed rather than folded

The paper that will not hold a crease

Every constraint these essays have found improves as the paper gets thinner: the stack, the size, the layer count. A crease does not. A crease is a plastic hinge in the fibres at the fold, and a sheet one fibre thick has nothing through its thickness to hinge — so there is a floor under the thickness that no manufacturing skill moves, because the fibre diameter is a constant of the plant. The papers a tradition folds sit between one and a half fibres and four, and the two below that in this collection's own shelf are tissues, which are backed with foil before anybody creases them.

history · Paper as substrate

Named alongside it

The objects these essays reach for when they reach for this one.

Crease radiusGoreIdealisationLayer countPaper thicknessSpherical capStrainSubstrateWet-folding

All concepts