Origami & Folding
what one sheet can do
Concept

Priority — where it appears

The question of who did something first, and whether the record can settle it. It is different again from who a result is named after, which is usually decided decades later by whoever wrote the textbook.

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

the alternating-angle conditionHusimi, 1979Kawasaki, 198910 yrmountains minus valleys is twoHusimi and Maekawa, 1979Justin, 19867 yrthe big-little-big lemmaJustin, 1986the lemma, 19948 yrone fold solves a cubicBeloch, 1936Huzita, 199155 yrthe diamond buckling patternYoshimura, 1951Yoshimura, 196918 yrthe bi-directional foldMiura, 1970Miura-ori, 199525 yr1940196019802000mean lag 21 years · longest 55proof

The name is not the date

Kawasaki's theorem is in Husimi's book ten years before Kawasaki's paper. Maekawa's is Justin's too. The mean gap between a result in this field and the name it is known by is twenty-two years, and it runs in one direction.

history · Attribution the cubic8x³ + 4x² − 4x − 1its roots-0.900969-0.2225210.6234903 real common tangentsone fold for each rootand the fold gives cos 2π/7each curve is the set of folds that puts one point on its line; a line touching both does the two at oncea compass intersects circles and gets two answers; a fold touches parabolas and gets up to three

Fifty years in the wrong language

Margherita Beloch showed in 1936 that one fold solves a general cubic. The result was correct, published, and in a mathematics journal — and the subject that needed it did not find it until 1991. The cost of a paper nobody reads is measurable, and it is most of a century.

history · Attribution

Named alongside it

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

AttributionBeloch's foldCubicEponymThe Huzita–Hatori axiomsIndependent discoveryKawasaki's theoremLill's methodMaekawa's theorem

All concepts