I think there's more basic opportunity for intuition and learning than pi/tau, which is using turns for angles. We tend to use degrees, which is less direct and

I think there's more basic opportunity for intuition and learning than pi/tau, which is using turns for angles. We tend to use degrees, which is less direct and requires memorisation/familiarity with magic numbers like 30, 45, 60, 90, 180, 720, etc. It takes more work to translate these numbers back and forth into angles (e.g. clock hands or pie charts) compared to twelfth, eighth, sixth, fourth, half, one, two, etc. turns. I think degrees should be left as a historical curiosity, like gradians, rather than the default we reach for in everyday life, from a young age (I can also see them being a nice 'mental maths shortcut', for those who are into such things). I know many people struggle with fractions, which degrees can avoid (at least, on a surface level), but I don't know whether the highly composite nature of 360 would help, and fractions hinder, outside of classroom-style exercises. For example, 90 + 45 = 135 is easier to calculate than 1/4 + 1/8 = 3/8, but the latter might still be more intuitive as an angle (e.g. if answering with a diagram, or by turning one's body); and for anything more complicated than that I'd still reach for a calculator, even with degrees. When problems require more sophistication than turns, we can introduce radians like we currently do. At that point tau makes sense as their conversion factor in equations, but it's still an unnecessary complexity when expressing angles; since any nice multiple of tau (or pi) can be divided through to get an even nicer number of turns.