The space-filling-curves tag has no wiki summary.

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### Hilbert Curve and Spatial properties [on hold]

I'm trying to understand the following proposition about the Hilbert Curves:
If (x,y) are the coordinates of a point within the unit square, and d
is the distance along the curve when it ...

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### Proof that no differentiable space-filling curve exists

Could someone provide a reference or a sketch of a proof that no differentiable space-filling curve exists?
Or piecewise differentiable?
Must every continuous space-filling curve be nowhere ...

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### Space filling curve to simplify vector addition? [closed]

Since points on a euclidean plane can be represented by one coordinate on a space-filling curve, is there any curve such that if two vectors $(x_0,y_0)$ and $(x_1,y_1)$ were represented by $a$ and ...

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### convexity of images of space-filling curves

Suppose $f:[0,1]\to[0,1]^2$ is continuous and for each $t\in[0,1]$, the area of $\lbrace f(s) : 0\le s\le t \rbrace$ is $t$. For what sets of values of $t\in[0,1]$ can $\lbrace f(s) : 0\le s\le t ...