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## Main Question or Discussion Point

Can one derive the approximate ratio between space and material in a ball with diameter B, wound of incompressible string with diameter s, where B>>s?

- Thread starter Loren Booda
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Can one derive the approximate ratio between space and material in a ball with diameter B, wound of incompressible string with diameter s, where B>>s?

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Would the string be randomly tangled, or wound in a precise pattern?

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HallsofIvy

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Also, string is taut.

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For an Archimedes spiral it is easy but when I move to 3D I get lost.

I would like to plot my ball of string in matlab. I'm happy to plot the string as a space curve (I don't need to show the string's diameter,

Actually my real goal is to fill 3D space with an expanding search path. Akin to spiral search in 2D.

I'm hanramo a t ho tmail com

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Perhaps knot theory could help?