The woes of the unit circle — a rant by my 15 year old daughterpic.twitter.com/y7UhTxiVp5
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Sounds like you should write that book! I am sure many would appreciate it. The best authors have a fire in their belly
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A very near approach to pedagogical optimality may be made simply by cribbing shamelessly from the great past masters (who, pretty much by definition, knew exactly what they were doing.) If it were up to me, I'd probably mostly just try to update Euler's notation and language.
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