3blue1brown

The scope creep of e and the hyperdarts puzzle

Hey everyone,

More on the animation above in just a moment.  There's no new video this month, but I thought I'd at least share some of what I'm working on.

The main project, whose writing has taken dramatically longer than I anticipated, is one likely to be titled "why e is overrated".  You may recall that in the e to the i pi in 3.14 minutes post, I mentioned wanting to pair t...

The windmill video is live (now with a real ending!)

Hi Everyone,

Thanks you for the feedback.  The final version of the video is now up.  Let me know what you think of the end, and do share it around with people you think might enjoy this kind of puzzle/lesson.

-Grant

(Early view) An unusual problem from the world's toughest high school math test

Hi Everyone,

Originally I was planning for the next video to be about e and generalized exponentiation.  That one is still in the works, but while I was a bit writers blocked on that one I turned to a different on on my list, outside the differential equations series, about a certain problem from the 2011 International Math Olympiad.

It will go public this Sunday, and in the meantime, I would benefit from a little insight from you all.  At the moment, there's no real end...

(Early view) Understanding e to the i pi in 3.14 minutes

Hi Everyone,

Alright, third video of the week!  For Patreon purposes, let's consider this video to be the first in a two-part project (i.e. this particular post will not be patron-supported), since it's rather short and the combined substance of this one with the next will be more akin to a typical 3b1b video.

Deviating from the usual 15-25 minute video tendency, the point of this one is to be as minimal as possible while still (hopefully) giving a well-paced explanation. &nb...

Bonus Fourier video (not a paid post)

Hey everyone,

As an addendum to the Fourier Series video, I put together many of the lots-of-vectors-drawing-something animations into a single montage.  No added math content here, but I hope you enjoy!

-Grant

Early view of Fourier series!

Hey everyone,

It's finally here.  I've teased the circle-drawing animations in the last two videos, and now we see the math behind it, and how it relates to the heat equation.  I still find it astounding that this idea originated in a piece of physics that, on its surface, has nothing to do with frequencies.

Let me know if you catch any errors (I haven't yet done a thorough comb-through for typos and such), the plan is to publish it this Sunday.

Also, for any $8+ p...

Solving the heat equation

At long last, a new video!

Ultimately I decided it's worth taking time on this one to not skim over things like boundary conditions, so the solution will be split into two videos.  This also gives some breathing room to better describe Fourier series not as a one-off tactic for this particular differential equation, but as a hint for something deeper, where decomposing a function into exponential parts (sine curves are exponentials in disguise) makes it easier to work with in the c...

Update

Hey everyone,

With you as the innermost circle of the 3b1b audience, the dominant source of my livelihood these days, and by any reasonable reckoning a part of the team, it seems only fitting to pass along the news that I got married this last Saturday.

It was a wonderful day, replete with the same kindness, beauty, and infectious happiness that could describe my now-wife on any day.  And, perhaps unsurprisingly, a subtle but persistent theme of math, and even the occasional ...

But what is a partial differential equation? | Overview of differential equations, chapter 2

Chapter 2 is out!  An initial look at PDEs, through the example of the heat equation.  Next chapter, we'll see how to solve it using Fourier series.

Usually this is the kind of thing I would have early released for Patrons, but I ended up running a bit behind schedule here.   Time constraints typically aren't a thing in my happy-go-lucky world of independent creation, but as mentioned at the end here I wanted to help promote Steve Strogatz's new book "Infinite powers...

It begins! Differential equations, chapter 1

Hi Everyone,

At long last, there is a new video.  And around half an hour at that.  This kicks off the series on differential equations, with a general overview of the topic, focused on a couple of specific examples from physics to love.

I remember how, as a student, most math classes I'd taken before ODEs focused on finding explicit solutions to problems, so my bias going in was that the primary goal to keep developing ever more intricate tools for finding such solution...

Release of Cramer's rule

Some of you may remember this video from several months back.  Now it's live!

Originally, I was planning on stacking up a few additions to the linear algebra series and releasing them as a little bundle, but I've decided to go ahead and just publish this one.  As mentioned in the last post, the plan is currently to do a miniseries on differential equations next, and I'll likely follow...

The coming of ODEs, and some transitive thanks

Hi everyone,

It's been a little while since I've posted a video, and the next video is likely still a couple of weeks out, so I thought I'd give a little update for anyone curious.

Last month I started writing what I hoped would be a small script on the idea of exponentiating a matrix, not in the sense of M^n, but of e^M.  Oh, silly me.  Drilling in on the questions of "why would you care?" and "what would you need know ahead of time?" has expanded it into several script...

Final block collision video! (Early view)

Edit: I replaced the link above with the updated (now public) version of the video.  Here's a link to the old, if you're curious.  Thank you all for the helpful corrections and suggestions!

---------

Hey everyone,

Here is an early view of the next and final block collision video.  Why make two videos solving one problem?  Because the tactic here is delightful!  It rea...

The solution is out! So why do colliding blocks compute pi?

Friends,

The solution is out!  Well, the first solution at any rate, I plan on doing one more video after this outlining Galperin’s original approach, which is arguably more beautiful. I chose to show the one above first since I think it’s more conducive to a “discover fiction” style narrative, hopefully making the viewer feel they could have discovered it themselves.

I kind of like this format of splitting what would usually be one video into a short opener showcasin...

New video (early view)

Hey everyone,

I hope you had an enjoyable holiday season.  I certainly did!  But I'm back to videos now, and quite excited about this current project.  Above you will find what I intend to be part 1 of 3, showing a truly mind-blowing phenomenon, while the next two will show alternate methods for explaining what is going on.  This will be published on Sunday, with the goal being that the following videos come one and two weeks after that respectively.

The goal h...

New video (early view): But *why* is a sphere's surface area four times its shadow?

Hey everyone!

Here's the draft of a new video.  The current plan is to publish it on Sunday, so I thought I'd share with you for any feedback you might have while I go through to clean a few things up.

I remember when I was a student being strangely unsatisfied with explanations of the surface are of a sphere that I had seen.  They either felt round about, or a bit like a black box, and (perhaps this was a personal quirk) I really wanted to know if the pi*R^2 showing up in the ...

Sneaky Topology

Hey Everyone,

I’ve been traveling a fair bit this month, so have had less time for usual video production.  To help fill the gap, I went back to do a refurbishing of an old video.  For one thing, it had a number of errors I wanted to correct, to include some typos, very poor sound quality, etc.  I also wanted to replace the proofy bit in the middle with a better argument, since the argument from the previous video was actually slightly incorrect, and now it ties nicely to the ...

Turbulence!

Hi everyone,

This latest project was part of a collaboration with Dianna Cowern, aka "Physics Girl", whose associated video you can find here.

As mentioned in the video, this all started out as an exploration of Vortex Rings, which is something Dianna covers more on the video she did, but I got caught up in how one of the methods we used for visualizing a cross section of these rings is actually an extremely nice illust...

Sneak peek for an upcoming video

Here's quick clip I wanted to share.  It involves taking a laser, diffracting it through a small glass rod so that the light is spread along a plane, and shooting smoke rings through that plane.

The explorable is live!

Full explorable series available here: https://eater.net/quaternions 

Thanks again for all your valuable feedback during the last month.  The comments here and the in-person conversations we had really helped to shape the experience.  I'm guessing it's still not perfect, with hundreds of alterations that could be made, but I'm happy with where it is now.  If you find this valuable, given that this medium ...

Early view of the "explorable videos"

Hey Everyone,

The quaternions follow-on is so close now.  We'll be publishing it this Friday.  I wanted to share a little sneak peek for you to take a look at (there will, of course, also be a YouTube video announcing this and pointing people to it, which I showed you in the last post).

Note: It's private right now, so resist the urge to use those social media links up top until I announce it this Friday.  At that point, though of course you should share like crazy :)

Quaternions and spatial rotation (beta)

Hey everyone,

Alright, three things for you in this post!  The video above is a sort of preamble into the main event.  That main event is a collaborative project done with Ben Eater, and it will be a kind of interactive video, where you can pause and play with the visuals at any point.  All web dev for this is thanks to Ben.

Right now, for the private/beta release, the interactive and the walk-thr...

Quaternions!

Hey everyone,

Early access time!  Here is the first installment of a rather large project I've been working on for quaternions.  I'm planning to publish it next Friday, and wanted to leave plenty of time to incorporate suggestions I get from you based on the early draft.

One question I have is whether or not more background on the history of Quaternions would be appreciated at the start.  The runtime is already rather long, so maybe it's better to err on the side of leavin...

Q&A rough cut

Hey folks,

I wanted to put out a Q&A episode this Friday, as a rather belated tribute to the 2^20 subscriber mark.

Here's the rough cut, and I was hoping to cut it down to something that lasts around 8 minutes.  Let me know which parts you find most worthy of ruthless exclusion!

(No charge here, of course, since it's not a lesson)

-Grant

New video (Early view)! Dandelin Spheres

Hey Everyone,

Here's an early view of the next video, one of my favorite little proofs from geometry relating two (or three) separate definitions of an ellipse.  The video is as much about why this proof is a good reflection of mathematical discovery in general as it is about the specific proof itself.  I hope you enjoy!

As always, feedback and comments are more than welcome.

-Grant

Feynman's lost lecture now live

Thanks for the feedback on the early release!

Early view of "Feynman's lost lecture"

Hey everyone!

Here’s an early view of a video for this Friday.  This one actually won’t go on 3blue1brown, but will be published to minutephysics as a guest video while Henry is on a long vacation.  For all intents and purposes, it’s a typical 3b1b video, just published to a different place for the win-win of more regular publication for Henry and more audience diversification for me.  Also, Henry has been the nicest person to me since the very early days of the channel, s...

So...what's the deal with probability?

Hey Everyone,

Several people have been (justifiably) curious about the status of the probability series, which makes it feel like a good time for another thought-dump via patreon post!

Basically, at the moment there are 5 videos which I feel, well, only so-so about.

1) Chapter 1
2) Combinations 2018-07-03 21:46:52 +0000 UTC View Post

50% off merchandise temporary fix

Hey $2+ patrons,

Some people alerted me to the fact that evidently the latest site update to DFTBA messed up the patrons-discounted price page that I had set up for you all.  As a temporary fix, we've just set up a simple discount code, "3b1bPatron", which you can use at checkout for any item in the main store, and it should give you 50% off.  Sorry about that!

-Grant

3b1b featured creators #1

Hey everyone!

In light of the 1,000,000 subscriber milestone, I wanted to quickly take the chance to acknowledge that much of the channel's growth came from a few very kind shout outs.  In the spirit of paying it forward, one thing I'd like to periodically do more is share the work of under-appreciated creators on the channel, so this is sort of an initial foray into that.

(No patron charge for a simple video like this)

-Grant