Fields
Axioms and construction
What a single fold can do, and why folding reaches numbers that a straightedge and compass cannot.
Flat-folding
When a crease pattern collapses flat — two local theorems, one global problem, and the gap between them.
Designing a base
Getting from a shape somebody wants to a crease pattern that produces it, by packing circles.
Tessellations
One vertex repeated until the sheet stops being a sheet and becomes a material.
Rigid folding
Panels and hinges instead of paper — the version that scales to solar arrays and stents.
Curves and material
Curved creases, developable surfaces, and everything the zero-thickness sheet was lying about.
What it costs to know
Deciding, counting, listing and optimising are four different questions about the same sheet, and folding answers them at four wildly different prices.
Who found it, and when
Almost everything repeated about where folding comes from is dated too early, attributed to the wrong person, or both. This field checks the claims against the record — and is honest that a record is not a proof.
Folding nobody designed
Leaves, wings and single strands of DNA all fold, and none of them were folded by anybody. Growth changes a sheet's own metric where a crease changes only its shape — the same geometry read in the opposite direction, and every figure here draws a fold this repository computed rather than an organism it did not measure.
Other ways through
a field is the coarsest of them
A field says what an essay is about, and every essay has exactly one. Everything else here cuts across it. A series groups essays by the idea each one makes an argument about, so a series is depth on a single idea rather than breadth over a subject — and several run through four or five fields at once, which is the useful thing about them. Threads are the motifs that recur in places with no business being related.
Two indexes are organised by artefact rather than by argument. Patterns lists every crease pattern this site can hand over — a sheet at true scale and a FOLD file for each, so the claim can be checked with paper rather than read. Figures lists the generators the pictures are drawn by, ordered by how many essays call each, with the theorems each one puts its own output past before it is allowed onto a page. Refutations is the shortest list and the sharpest: everything widely repeated about folding that this site tested and found wanting, with what decided each one.