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What's your vision for how the centre hole will look when closed? If you're happy with a slot, a top 125mm will do.
If you want an infinitely small hole (let's ignore the practicalities of the material, the corners need to be the length of half the diagonal, which you can get by pythagoras - square root of (a squared plus b squared)
And that also gives you the shape of the curve, where a is the distance from the centre of the edge you're drawing and b is half the length of the other side.
ETA: Curve of the long side https://www.desmos.com/calculator/fkuqjnmsqd
grams
@moocher
Geometry question:
I have rectangular mouthed bag 510 x 250mm, into which I want to sew a drawstring top, this would close up to be a rectangle fitting the top.
When open it is in effect an extension upwards of the existing bag.
Maximum length of material needed is therefore 280mm (which is half 0f 560 - the long side of the triangle). This will be too much material elsewhere - coming in from the midpoint of the long side to the middle is only 125.
Presumably, the change from longest to smallest is a straight line (blue)? If it is a curve (orange), what kind of curve??
Diagram attached will make all clear.
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