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Seen via +Malin Christersson: A spectacular-looking website explains complex numbers and some of the things they're good for, including a remarkable visualization of how a Julia-set fractal is made, and another of how complex numbers are used to analyze wave phenomena in physics and engineering.

This is stuff that it took me years to learn how to visualize intuitively, displayed all in one place with animations. I also like the remarks at the beginning about the problems with how we present mathematics to students, and turn beautiful things into unpleasant experiences.

My only criticisms are that (1) the site is technically demanding, probably requires a recent browser and might push yours pretty hard (my laptop's fan was running the whole time I was looking at it), and (2) it was initially not obvious to me how to start reading the article (just scroll down as usual).
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Also, I like that it opens with a quote from Hogfather (we were just re-watching the TV-movie adaptation).
He mentions in his talk that the 3D web site is a bit ridiculous. 
If you try to push web-technology forward, as he is doing, you can't make a web site that is viewable from old browsers.
I also wonder about accessibility for the blind and visually-impaired, but that is a problem for any mathematical presentation that is highly visual.
...And at the moment when he moved the positive real axis to the top and surreptitiously flipped the whole complex plane so that positive angles went clockwise, I flinched. But that was just the fusty conventionalist in me.
Yeah, even I have a problem with positive angles going clockwise. :D
I gave a talk a couple of years ago, and I noticed that a blind man was sitting in the front row. After that I tried to reconsider my way of doing but presentations, but I came to the conclusion that it is simply not possible to make visual math accessible for the visually impaired. :(
I think you actually can, with physical tactile models and possibly other ways of presenting spatial information. But the technology isn't there yet to make this really easy for web presentations or lectures.
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