Origami & Folding
what one sheet can do
Concept

Systematic error — where it appears

An error that is the same at every measurement rather than scattered about the truth. It does not average out, more data does not reduce it, and it is invisible to every check made within the measurement — so it is found by comparing against something computed a different way, or against a bound it should not exceed.

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

05101520253000.050.10.150.20.250.3creasesdrift, in panel widthsthe same way each timeat randomeach crease 0.5° out · 40 strips averaged for the random casethe drift is a composition of reflections, and would be the same on paper

Error is folded too

A folded position is a composition of reflections, and a reflection in a line that is slightly off turns everything beyond it by twice as much. So an error does not stay where it was made — and whether it grows with the crease count or with its square root depends on whether it is the same error every time.

rigid · Tolerance the length a pattern reports, and the length a sheet of paper hassix of the eight are built on a unit square, so on those the distinction does not arisepatternown widthraw lengthreportedon paperThe Miura fold6.3739.36,6791,049out by 6.37xThe tapered corrugation1.187.81,2431,057out by 1.18xThe preliminary base1.004.8724724the sameThe square twist1.004.7704704the sameThe hexagon twist1.006.1916916the sameThe Yoshimura pattern1.0014.02,3802,380the sameFold and cut — the triangle1.001.7258258the sameThe waterbomb tessellation1.0014.32,2902,290the samea builder working in cells returns a pattern several units across, and not dividing by that is the whole of the error

A length needs a scale

These essays measure crease length, and a crease length is a length in the pattern's own coordinates. Six of the eight printed patterns are built on a unit square, so their coordinates are sheet widths and the distinction never arises. Two are not — a Miura laid out as six cells of unit width spans 6.37 — and on those two the shelf multiplied by the printed size without dividing by the width. The Miura's folding length was reported as 6,679 millimetres and is 1,049, and the same pattern's printable sheet has carried the right number all along.

material · Crease density

Named alongside it

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

Crease densityCrease lengthCrease patternError propagationIdealisationManufacturingMeasurementReflectionReproducibilityTolerance

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