Full winding numbers video

There is not necessarily a zero.

Jacob Mirra

Fantastic

michael bukachi

Really awesome

Lust and Kinky Games

Wonder if we can apply this to micro strips to determine the impedance.

So question- what does it mean if the winding number of a region is 0?

Tomás Tomcat

A really good (and fun!) talk by the Matplotlib people on how they determined their new, more colourblind-friendly, colour maps: <a href="https://www.youtube.com/watch?v=xAoljeRJ3lU" rel="nofollow noopener" target="_blank">"A Better Default Colormap for Matplotlib | SciPy 2015 | Nathaniel Smith and Stéfan van der Walt"</a> <a href="https://www.youtube.com/watch?v=xAoljeRJ3lU" rel="nofollow noopener" target="_blank">https://www.youtube.com/watch?v=xAoljeRJ3lU</a> The resulting colourmaps can be found in matplotlib: <a href="https://matplotlib.org/tutorials/colors/colormaps.html#sphx-glr-tutorials-colors-colormaps-py" rel="nofollow noopener" target="_blank">https://matplotlib.org/tutorials/colors/colormaps.html#sphx-glr-tutorials-colors-colormaps-py</a> (I recall that you use Python for your animations, so matplotlib needs no introduction, but I added the link for convenience) They also have some really neat tools to build your own colour maps and test how colourblind-friendly they are, the linked video describes them.

Job van der Zwan

As an aside, there was some discussion in the YT comments about colourblind-friendliness of the video, with the consensus being "it's not a hurdle in this case due to context and alternative explanations". Being colourblind myself I agree with that, but I figure it won't hurt to share some links to some really good tools to make life easier for the colourblind. There are some very pretty palettes out there that are easier to see by almost everyone!

Job van der Zwan

Hmm, interesting question. So, typically the advantage of an interpolation search comes when you have a notion not just of one end being too low and another too high, but also how far off they are, right? Perhaps if you were willing to make certain assumptions about the 2d function you're dealing with (e.g. that the direction of the output changes more quickly around zeros), you could do something similar by narrowing in more closely on regions where the boundary included quick changes to the output.

3blue1brown

A valid question, given that many other tactics for finding numerical solutions leverage differential properties of some kind. But in this case, continuity alone is enough for this to work.

3blue1brown

I'll ask the same question here I posted on the youtube channel: if this is a 2D "binary search", could one also create a 2D "interpolation search"? Or does that run into new problems yet again?

Job van der Zwan

This reminds me of a moment in a summer program I attended many years ago. The professor was going over some number theory idea and conjectured something right on the board in front of us, then proposed that we test it with N=7. It did not work, so he amended the statement to "For all N, except 7,..." and everyone laughed. Except it turned out that the altered statement was actually true.

Kevin

I love that in this video you deliberately lead the audience to believe in a hypothesis, and then unexpectedly disprove the hypothesis and replace it with a better one. Students are used to consuming information about proven facts; they're not expected to validate information beyond understanding it. Instead, not knowing whether a presented piece of information is true or not requires active thinking on the student's part to test and predict whether an observation is correct as they're learning it. Furthermore, "getting it wrong the first time" makes the correct conclusion more memorable.

Really like how you went through a failed solution, even as someone accomplished in a mathematical field where this kind of experimentation is commonplace in solving problems, it really made the topic feel more approachable; I can only imagine how helpful that must be for someone currently in school.

Robert Lamacraft

Awesome one) Looks so colorful, like that one <a href="https://www.youtube.com/watch?v=IjIViETya5k" rel="nofollow noopener" target="_blank">https://www.youtube.com/watch?v=IjIViETya5k</a>

1D_Inc

Continuous suffices, provided you know the modulus of uniform continuity over the region you are analyzing. Grant even mentioned something below the video to the effect that the number of points you have to sample depends on this continuity. So I think this is all mathematically sound. Edit: I guess I should say "3Blue1Brown mentioned..." since this is turning into an organization. Who knows, perhaps some PR person will be doing YouTube comments before long.

Jacob Mirra

Don't you think the function you examine has to be differentiable, not only continuous?

Lech Mankiewicz