Normally I'd just upvote and move on, but this is really fucking good. For example, I wish I could have seen something like that "Sine Wave Aliasing" page when I was learning this stuff, would have saved me a lot of confusion.
The quaternions are a subalgebra of geometric algebra. It's not quite the same in that it's strictly more general and, therefore, more broadly applicable.
This is awesome. Congratulations! It should be thrown in the face of the textbook publishing industry that still charges $100+ dollars for yearly reprints of paper bricks.
This is what the textbooks should be in the 21st century! Outstanding work and hopefully it will inspire new generation of academics to take the outdated textbook publishing monopolies out of the loop in the future.
I wish they could have done things like this when I was learning signals and transforms as an undergrad. But interactive didn't really exist in the early 90s.
As a side note, the pressure that is waxing and waning in that diagram is very very small compared to atmospheric pressure.
The actual air molecules are moving at a much higher speed (the root mean squared velocity is dependent on the temperature). But if we imagine that these are weightless dust particles suspended in air, the diagram is accurate.
Like!! It took me a while to chew through signals and FT back in school (before the web) so I really appreciate how this is bringing browser-based animations to the general public. It's a lot easier to understand that way.
This is a wonderful piece of work. Exceptionally clear writing and excellent use of interactivity.
One minor bug report, the mathematical pi symbol (U+1D6D1) used in the unit circle doesn't appear to be displayed correctly (Chrome 40, Windows 7): https://i.imgur.com/zt0HDLO.png. It's okay in Firefox though.
Wow, that really means a lot. Thank you! Really glad to hear that you are finding it useful. Please send along your feedback and questions if anything doesn't make sense or is poorly communicated in the text/visualizations.
It seems like the equation processing gets messed late in section 4 - $$ \mathrm{DFT}[k] = \sum_{n=0}^{N-1} \mathrm{x}[n] \cdot (cos(\varphi) - sin(\varphi)i) \\ where \quad \varphi = k \frac{n}{N} 2\pi $$
That's because you're accessing the site from HTTPS, or you have HTTPS Everywhere installed which is doing it for you. I think he's loading MathJax as HTTP, which means it gets blocked because it's coming from an insecure connection.
This is incredible. I wish more professors in universities incorporated this stuff in their teaching. I occasionally use Wolfram Demonstrations: http://demonstrations.wolfram.com/
But you take it to another level! Congratulations!
Did you use a tool to make the interactive diagrams, or just write all of them by hand?
(I can imagine myself forever tweaking each diagram, and having to cut back on them, but you've created them everywhere they might be useful - it's a fantastic site)
Hi Jack, awesome work! Did you write the HTML by hand or did you use or write some static generator? I'd love to have sidenotes like yours automatically generated and positioned.
I can't speak to how he did it, but it looks like he's just using tables and line breaks & divs to separate sections. You could easily do that by hand.
Alternately, you could use Bret Victor's technique from "Magic Ink": write a paragraph followed by a span, typically with absolute positioning. http://worrydream.com/#!/MagicInk
