Lines have no thickness so one would imagine curves don't fill space. But this guy argues in the limit of 'passing through every point', curves can fill spaces...
And it's a half-interesting use of a 3-d printer...
a paradox resolved by 3d printing
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Rumraket wrote:This thread is not what was advertised.
igorfrankensteen wrote:I'm not seeing the "space filling." Rather misleading title, whot?
CdesignProponentsist wrote:igorfrankensteen wrote:I'm not seeing the "space filling." Rather misleading title, whot?
They are called space filling because as length increases with each iteration, the area they fill remains constant and when taken to infinite iterations occupies all points within that space.
You can also say that they completely fill space in a finite number of iterations where space is quantized. Like a sheet of graph paper where you fill in every single square in the sheet while following the curve.
Lines have no thickness.
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