I cannot help myself from saying something about sundials, since one of my mathematical models is in fact the simplest sundial (Jackie...)
I took me a lot of time to know that sundials work because
the gnomon is parallel to the the South North axis
So, imagine that the gnomon IS that axis, and imagine a plane tangent (=touching) the earth in the North Pole, divided in 24 equal angles.
Well, with some approximation, it should be clear that the shadow of the axis runs around, covering one of these angles in exactly an hour.