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.

Hi, e!
Oh! I couldn't imagine why you posted about this word, then the light dawned when I thought to check the WAD.
You made a model of THIS? Cool! (By the way, I have been
extolling your virtues to someone lately--heh heh heh.)

I had to re-read your post to finally be able to picture
(I hope) what you were describing. I don't have a particularly mathematical turn of mind, and so I still can't picture what has happened according to the WAD's
second definition: "2. The remaining part of a parallelogram after a similar smaller parallelogram has been taken away from one of the corners."
Um--should I be picturing a parallelogram with two complete sides and two partial sides?

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.

I was about to ask how you could read it at night to prove that it works for each hour. But, of course, you'd be able to use a torch to see, wouldn't you? [running-like-hell emoticon]

It is obvious that is an ideal model, not caring about the slope of the earth - so imagining that the axis of rotation of the earth is perpendicular to the plane in which the earth rotates around the sun.
In this model, since the sun is bigger of the earth, there is no night at the poles...

Does this mean that the elephants on whose back the earth is balanced are in perpetual sunlight? Or are the two currently furthest from the sun in the nightshade of the two that are nearest?