Origami & Folding
what one sheet can do
Concept

Provenance — where it appears

What a claim about the past actually rests on: which source, of what kind, and how many independent ones. It is recorded separately from the claim itself, because the difference between a date and the oldest surviving evidence for that date is the whole of this subject's history.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

patternclassdatedfoldingThe preliminary basetraditional—724 mmThe Miura foldpublished as mathematics19701049 mmThe square twistgenerated here—704 mmThe hexagon twistgenerated here—916 mmThe Yoshimura patternpublished as mathematics19552380 mmFold and cut — the trianglegenerated here—258 mmThe tapered corrugationgenerated here—1057 mmThe waterbomb tessellationtraditional—2290 mm2 dated, all of them published; 6 undated, none of them ownedthe fourth class — a designer's model — is what this shelf holds none of

The patterns nobody owns

This site prints crease patterns at true scale and prints no designer's work, and that has always been stated as a rule applied at the end. Read the printed shelf as a documentary record instead and the rule turns out to be a property of the record: every pattern that carries a date was published as mathematics, every undated one belongs to nobody, and the two silences are one silence.

history · Attribution each mark is one claim: right of the line means dated earlier than its evidencethe vertical line is agreement between the claim and the record0paper itselfwhen and where the material was made, which is archaeologymedian 0 · spread 204a thing people dida fold, a ceremony, a toy, a lesson — something with no first daymedian 347 · spread 979a thing somebody proved or designeda statement with a paper, a date and an authormedian -14 · spread 131

Two kinds of claim

This site has published a median overrun of two centuries and a mean of twenty-two years in the opposite direction, and both are right. Split the record by what each claim is about and the reason appears: every claim about a practice is dated earlier than its evidence, most claims about a result are dated later, and the two scatter by 979 years and 131.

history · Attribution a disc, with a vertexa ring, with noneone interior vertex, 3 creases at itodd degree, so they do notno interior vertices at alland the panels still do notboth refuse: two routes round the sheet leave a panel 1.87 sheet-widths apart

A theorem with an unstated hypothesis

Maekawa's and Kawasaki's conditions are quoted everywhere without saying which sheet they are about, and they do not need to be — they are conditions at a point and every point is the same. The two-colouring is quoted the same way and it is not a condition at a point, and the omission there is not harmless.

history · Attribution

Named alongside it

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

AttributionDocumentary recordBoundaryCrease patternFolkloreGluingKawasaki's theoremLocalityMaekawa's theoremPublicationRediscoveryTradition

All concepts