Origami & Folding
what one sheet can do
Concept

Froebel — where it appears

The educator who put paper folding into European kindergartens as geometry rather than as craft. His three categories of fold divide the activity by what it is for, which is a classification the subject still carries.

Named by 4 essays across one field — each of them below, with the objects they name alongside it.

3 equal partsestimated by eyethe left-hand divisions are exact — a consequence of the fold, not of carethe right-hand ones are a guess, and the error compoundsvalleymountain

The kindergarten was a geometry class

Froebel put paper folding into mass education in the 1830s, and did it as mathematics rather than as craft. His three categories — the folds of life, of beauty, and of knowledge — are the first systematic treatment of folding anybody wrote down, and the third one is a geometry syllabus.

history · Pedagogy Folded paper is used ceremonially in Japan400 yrPaper is folded for amusement in Japan980 yrThe thousand cranes897 yrThe pajarita is folded in Spain293 yrPaper folding is taught as geometryyear of the source500100015002000the date generally giventhe oldest source that says somedian overrun 400 years

Two traditions and a merge

Ceremonial wrapping, recreational folding and the kindergarten syllabus are three separate lineages with three separate purposes, and they were independent until the late nineteenth century. Told as one continuous tradition, the oldest date in any of them becomes the age of all three.

history · Two traditions the year the record can put two lineages in the same worldthe later of two surviving sources, which is what a joint claim rests onFolded paper is used ceremoniawith paper is folded for amusement 1680Folded paper is used ceremoniawith the pajarita is folded in spai1793Paper is folded for amusement with the pajarita is folded in spai1793Folded paper is used ceremoniawith the thousand cranes1797Paper is folded for amusement with the thousand cranes1797The thousand craneswith the pajarita is folded in spai1797Folded paper is used ceremoniawith paper folding is taught as geo1838Paper is folded for amusement with paper folding is taught as geo1838The thousand craneswith paper folding is taught as geo1838The pajarita is folded in Spaiwith paper folding is taught as geo1838all 5 are jointly attested only from 1838 — every earlier joint claim is a claim about at most 4 of themeach row is the later of two surviving sources · Paper folding is taught as geometry at 1838 is what the whole set waits for

When two of them are first attested together

Every single date in this field is argued about by centuries, and a pairwise one is not. The earliest year at which two claims are both attested is simply the later of their two surviving sources, so it inherits the better-attested half of each pair rather than the worse — and the year at which all five lineages of practice are jointly on the record is 1838, one year from where the same claims are popularly dated together.

history · Two traditions the year all 5 lineages are on the record, over 20,000 resamplingseach resample draws the lineages with replacement and takes the latest earliest source among those drawnafter 18380.0%no resample can hold a source the record does not183867.1%froebel, 4 witnesses179725.5%senbazuru, one witness17936.4%pajarita, 2 witnesses16800.9%recreational-folding, one witness67.1% return 1838 exactly; the chance a draw of 5 includes the holder is 1 − (1 − 1⁄5)^5 = 67.2%

A resampled maximum can only fall

The joint date of paper folding's five lineages is 1838, and resampling the record twenty thousand times returns 1838 in two draws of three and an earlier year in the rest — never a later one. That is not firmness. It is the chance that a draw of five from five includes one named entry, and it is the reason a resampled interval cannot be put on a maximum at all. Read over all 105 pairs in the record, a joint date inherits the later half of its pair, not the better-attested one: the better in 46, the worse in 35, and a single surviving witness in 28.

history · Two traditions

Named alongside it

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

AttestationDocumentary recordNoshiPajaritaPrimary sourceCeremonial wrappingConstructive proofExact divisionExpected-valueFujimoto's methodIndependencePedagogy

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