A straight line (y=x) can be written as a sum over sinusoids, known as a Fourier Series.pic.twitter.com/Obii1qd62T
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that's right, it converges to y=x in (-π,π) for the Fourier series (as opposed to the transform). Given that it does converge to a line on (-π,π), i wouldn't say i fibbed.. This is twitter,not an academic conference.The purpose of my tweets is to get across the basic idea in..
a neat way and .. if people are curious/want to know more they can pursue it by either asking questions or going to learn it on their own.. Presumably, you know this and that throwing a bunch of conditions at people isn't the best way to engage people
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Is teaching kids Newtonian mechanics fibbing, or should we also tell them that it's only valid in the domain of weak gravitational force (i mean spacetime curvature).. but actually /that's/ not quite true when we consider QM as well.. i wish you good luck with that curriculum
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I teach all my Twitter kids about curved spacetime in the fully nonlinear regime.
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I’m all for popularizing fascinating math ideas (wasn’t trying to disparage), of which Fourier series is certainly one, but from reading some of the comments, people seemed rather confused about (and interested in!) what was going on near the endpoints, with good reason...
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there is some detail omitted, as i didn't specify that the boundary conditions enforce the vanishing of the series on the endpoints.. wasn't sure how to make that digestible and wasn't sure if whether or not it'd be helpful trying to explain it in the main tweet
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Thanks. Twitter will use this to make your timeline better. UndoUndo
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