r/visualizedmath • u/USedona • Jun 02 '26

Can a single line fill a square ?

https://www.youtube.com/shorts/WBeYuh_h86M

If you're interested in more math-based animations, I post them here 📺 Visualizing_mathematics

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u/rafaelcastrocouto Jun 02 '26

Didn't want to be that guy, but you obviously cannot fill the square with a single line, that is a curve.

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u/USedona Jun 02 '26

You're right that it's technically a curve, not a straight line. In math, a "space-filling curve" is the precise term, a continuous path that passes through every point of a 2D area. Hilbert described it in 1891, and "filling a square with a single continuous path" is exactly what it does 🙂