Think about the context here, though. Having a symbol for 2pi would be much more convenient because it would make things consistent. 2pi is the number that you typically cut into fractions. Let's say we define, say, rho to mean 2pi. Then we have rho, rho/2, rho/3, rho/4... whereas with pi, we have 2pi, 2pi/2, 2pi/3, 2pi/4... the problem is those even numbers. Writing 2pi/4 looks ugly, you want to simplify, but writing pi/2 means that you no longer see the number "4" there, which is what's important, that it's a quarter of 2pi. You see the "2" on the bottom so you think it's half of 2pi. It's a mistake everyone makes every now and then - seeing pi/n and thinking it's 2pi/n. If we just had a symbol for 2pi, this wouldn't occur. Other mistakes would, sure, but as commonly as this one does?
If we were to define, say, xi=pi/2, then 4xi, 2xi, 4xi/3, xi, 4xi/5... well, that's just awful.
It's a mistake everyone makes every now and then - seeing pi/n and thinking it's 2pi/n.
What? Like who, 6th graders?
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