Origami & Folding
what one sheet can do
Generator

The hole a curved pleat leaves

A generator in the curves and material library, called 7 times across 1 essay. Below: what it draws with nothing specified and with the settings the essays give it, what it checked while drawing, and everywhere it is used.

pleat-hole is one function. Everything below was drawn by it when the site was last published, at settings taken from the essays rather than invented for this page — so a figure here is the same figure a reader meets in an essay, and when the generator changes, this page changes with it.

With nothing specified

The hole a curved pleat leavesConcentric circular creases at a fixed spacing, drawn inward until the paper between two of them can no longer exist. The shaded disc is what is left: its radius is set by the spacing and the ruling angle, and by nothing about the sheet.17%7 circles fit; the middle 17 per cent cannot carry anyspacing 0.06, rulings at 0.9 radians to the crease

view: "pattern", outer: 0.45, w: 0.06, beta: 0.9

The hole a curved pleat leavesConcentric circular creases at a fixed spacing, drawn inward until the paper between two of them can no longer exist. The shaded disc is what is left: its radius is set by the spacing and the ruling angle, and by nothing about the sheet.17%7 circles fit; the middle 17 per cent cannot carry anyspacing 0.06, rulings at 0.9 radians to the crease

view: "pattern", outer: 0.45, w: 0.09, beta: 0.6

The hole a curved pleat leavesConcentric circular creases at a fixed spacing, drawn inward until the paper between two of them can no longer exist. The shaded disc is what is left: its radius is set by the spacing and the ruling angle, and by nothing about the sheet.35%4 circles fit; the middle 35 per cent cannot carry anyspacing 0.09, rulings at 0.6 radians to the crease

view: "sheets", outer: 0.45, w: 0.06, beta: 0.9

The same hole on both sheetsThe same pleat spacing on a small sheet and on one twice its size, drawn to the same scale. The large sheet takes twice as many circles and leaves a hole of exactly the same radius.a small sheet4 circlestwice the radius10 circlesboth stop at a radius of 0.077

What it checked while it drew

Collected while it drew, not written by hand. The count is how many separate times that claim was put to the test.

Where it is called

Every figure listed here is drawn by the same rule, so a mistake in the rule would be in all of them at once, and so would a correction.

The gap between two curves

The rulings leaving a curved crease are not parallel, so they cross, and the surface exists only as far as the first crossing. That bound is usually read as a limit on how far a design extends outward. It is not: the paper between two curved creases has to be reachable from both, so the bound bites hardest where the circles are smallest, and a concentric pleat has a hole in the middle that no sheet size removes.

All the figures · The curves and material field · The patterns a reader can fold