Suppose a radius sweeps a semihexagon inscribed in a semicircle.
Has it swept $180\unicode{xb0}$ (semicircle) or $360\unicode{xb0}$ (semihexagon)?
2026-03-25 06:01:20.1774418480
Differing notions of 'degrees' in 2D polygons
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On reflection, I think this shows that degrees swept by one end of a line may differ from degrees swept by the other end in the same movement.
To make this more obvious, imagine the semihexagon is instead a sinewave. Each period has $360\unicode{xb0}$, and there is no limit to the number of periods that can be squeezed around the circumference of the semicircle.
So the inner end of the line sweeps $180\unicode{xb0}$, while the outer end sweeps anywhere up to $\infty\unicode{xb0}$. There are multiple circumferential degrees per central degree, if you like.