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I'd like to propose bytians - a "new" angular measurement system which uses 256 divisions of a circle.

Full circle - 256 bytians
Half circle - 128 bytians
Right angle - 64 bytians
Diagonal - 32 bytians

We lose nice triangular angles, where 60° = 42.66... bytians. More exactly, this would be 128/3 bytians.

(Also, this has to have been done before)

@dl
Doom source does this and calls it BAM (binary angle measurement). Useful because you can use an integer type for angles and take the top bits to do fast trig table lookups

@dl What benefits does that have over degrees?

360 is nice because it has more than one prime divisor; it's divisible by 2 (three times), 3 (twice), and 5. The sexagesimal Babylonian number system has that property as well, which is probably why we divide hours and minutes that way. As Wikipedia puts it: "60 is the smallest number that is divisible by every number from 1 to 6". This is a really useful property!

(Base 30 might be nice for math, or lacking that, base 12.)

@dl Got it, so you get precision and performance in computing. Neat!

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