zero_call comments on Open Thread: March 2010, part 2 - Less Wrong
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What? Like who, 6th graders?
I find that unfair. I have made the mistake Sniffnoy describes many times, all of them after I was in 6th grade.
Easy solution. Pi is half a circle. Pie is the whole one. Then there is a smooth transition from grade 3 to university.
I've been looking for a good thing to call 2*Pi - this might cut it.
Nice one! ;)
No, like anyone who isn't watching out for traps caused by bad notation. It's much easier to copy down numbers than it is to alter them appropriately. If you see "e^(pi * i/3)", what stands out is the 3 in the denominator. Except oops, pi actually only means half a circle, so this is a sixth root of unity, not a third one. Part of why I like to just write zeta_n instead of e^(2pi * i/n). Sure, this can be avoided with a bit of thought, but thought shouldn't be required here; notation that forces you to think about something so trivial, is not good notation.
omega_n is the notation I most often run across.
Hm, I've generally just seen omega for zeta_3.
I've certainly used it for that -- but I pattern it with dropping the subscript n, when it is clear when there is only one particular root of unity we're basing off of. I've never ever seen zeta used.