Chip-firing games and sesquinary notation:

Jim Propp writes a monthly long-form math blog and somehow I hadn't encountered it before. This is one of its many interesting entries. One of the oddities about base 3/2 is that you calculate it bottom-up (by starting from a ones digit that's too big and then carrying things higher) instead of top-down (by greedily subtracting powers).

@11011110 Things get particularly weird (and wonderful) when your fractional base is smaller than 1. You can see a problem about inserting things into a rotating queue that leads to these kinds of expansions in these slides:

@11011110 A student of mine wrote an undergraduate thesis (in a more formal style) on the rotating queue and fractional base expansions here:

There's a section about positional arithmetic where addition is not just "add with carry" but "add with carry that persists forever," which I've always wanted to share with a bigger audience, because it's neat.

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