So y'know how we did a stream last week where we calculated the golden ratio in a bunch of different bases to see how doing arithmetic by hand felt? https://www.twitch.tv/videos/879810768 And remember how we said that we were thinking of doing another arithmetic stream sometime?
So, @fae has brought to our attention a really great suggestion that we are going to generalize slightly: doing long division in /non/-standard positional number systems. Fae specifically mentioned quater-imaginary, base 2i - https://en.wikipedia.org/wiki/Quater-imaginary_base - but there are a few others with Wikipedia pages (e.g. balanced ternary, factorial number system, golden ratio base) and we could probably spend a nice length of stream playing with them.
It'd be interesting! I'm kind of excited at the idea.
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@packbat another variant might be working thru examples of the sunzi theorem / "chinese remainder theorem," which is kind of like if each digit is a different base :D https://en.wikipedia.org/wiki/Chinese_remainder_theorem
@fae *nods!*
we were planning on giving the factorial number system a try, which is literally each digit being a different base; it'd be interesting comparing that experience to the sunzi theorem!
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@packbat (that's... an inaccurate summary but, anyway it's a neat construction ^^)