Early view of "Feynman's lost lecture"

Thanks so much!

3blue1brown

The Feynman's video is superb. Thanks for your work.

I talk about it on the FAQ page: <a href="http://www.3blue1brown.com/about" rel="nofollow noopener" target="_blank">http://www.3blue1brown.com/about</a>

3blue1brown

how do you do this math animations? what software do you use?

Job well done.

Awesome video! I would have also loved a comment about what determines the size of the ellipse and the positions of the foci of the ellipse..

Hey, sorry I didn't see this earlier. This is a good suggestion, but I already re-uploaded a version with some fixes based on other comments here, and given the coordination logistics of doing it as a guest video this particular change might be a little too small for the hassle. It'll be good to keep in mind the need for constant indication in future animations though!

3blue1brown

I wish you had summarized the assumptions that we started with and upon which all this was based (since that's what made it "elementary"). Is it just kepler's 2nd law and the inverse square law?

First off, I really like the overview screen at 1:00. At 20:00 you don't wiggle the radial line or eccentric line when you reference them. Moving the other lines and animating the intersection point when you mentioned them made it much easier to follow, and I kind of got lost when it stopped happening. Also, not sure if it’s needed, but you never directly state that the yellow vectors at 15:25 are Delta V. Great video as always!

Ah, good point, I think I had originally written this while imagining pinning down two ends of a string, before realizing how tricky that ended up being when doing it in practice.

3blue1brown

Thanks Nitai, good catch on the visual bug. Hopefully the argument doesn't prove too tricky for most people. I had a similar sensation of rewinding (well, re-reading in my case) multiple times while originally going through it, but so satisfied in the end I really wanted to share the conclusion with others.

3blue1brown

Thanks for the feedback Osamah. Hmm, is it the point about the two congruent triangles that is unclear? What do you think, should I maybe talk through the relevant SAS congruency more explicitly?

3blue1brown

Thanks so much!

3blue1brown

I've been a "silent" patreon for a while now, enjoying your videos very much, forwarding them to my students in the "introduction to computer graphics" course every now and then to get a better visual understanding of what their working with. But this video is utterly beautiful and really made me stop and sigh while going through it. Great job, once again.

I prefer videos about pure mathematics and computer science, but I do get that you might think differently.

Ooh, good catch, I didn't even notice I said that.

3blue1brown

Beautiful!One small comment - at around 7:40, you refer to two similar triangles, when you probably mean congruent triangles

Edith Dubiner

You said that the two triangles in the proof of the focal sum are "similar." Aren't they actually "congruent?" It is their congruency that assures that sum of the distance from the foci = (center to Q) + (Q to P).

I think that the sum of the distances from the two thumb tacks is the length of the string, MINUS THE DISTANCE BETWEEN THE THUMB TACKS, which is the length of the straight part connecting the thumb tacks.

You have outdone yourself again! Just an amazing video.

Wow, those 20min are packed steeply! Can we haz more Geometry Proof Land?

slzb

Make sure to get the new edition from Kronecker-Wallis!

slzb

I agree, "this shape satisfies this property" doesn't convince me that this is the ONLY shape that does.

This is fantastic. The only step I found to be a little "jumpy" is the final one, where you claimed because the two curves have the same "tangency property", they are the same shape.

Chenfeng Bao

I love it. I did have to rewind a few times, but as you say repeatedly, a lot of focus and "infinite intelligence" is needed here so I never felt bad about it. I did find a minor visual error though: at 13:41 and again at 13:56, "(Radius)²" appears - you probably want only the 13:56 one. I said this on the YouTube comments already but I don't know if you notice them.

Hey Grant, I really could not follow you at your statement at 7:36 ("Adding the distances to each focus is the same as adding the distance from the center to Q and then from Q to P") I understand what you said but not why its true. Perhaps if you used some extra visual techniques (highlighting the distances you mentioned) could be helpful? Awesome video though! I love it

Love this! At 7:25, when you justify why the two distances are equal, it is better to use the word congruent, rather than similar. Of course, all congruent triangles are also similar, but it is not the similarity, but the congruency, that makes the distances equal.

I really like it, but it is a lot to cover in 20 minutes. I think the geometric proof is really nicely explained, as is the Kepler+inverse square leading to the constant velocity change. In my opinion, the way you invoke the conservation of angular momentum is too rushed. I would give angular momentum a more complete introduction so it seems less like a "sky hook". The final argument relating the velocity diagram to the orbit shape ends up having a lot of jargon. I might try to clarify the writing of that last step.

Gabe

I suppose this is better than the vector analysis-style proof you usually get: “Take the dot product of these two vectors! Integrate! Take the cross product of these! Integrate! Do a lot of algebra! Apply polar coordinates! Done!” I kind of want to read Principia now. Nice video.

Jacob Mirra

Beautiful!

Daniel Armesto

Always amazing. I too seem to have been pronouncing 'foci' wrong. At 5:23, the footnote that comes up vanished a little fast for me to read it.

Always so much fun. Thanks Grant!

Caleb Pheloung

It was a little unexpected hearing you pronounce the c's in "foci" and "principia" the exact opposite of how I would do it, but I'm not a native speaker and apparently both are correct, so... yeah.

wye

Magistral. Superb. Publish in your channel too. One thing: At 19:42 circa, the order in which you say “two lines...” and you highlight both simultaneously, you are saying one “from the centre” and “one offset”, the one from the centre is to the right of the one offset. It would be clearer to make the from the centre vibrate first, then the one from the offset (which is to the left of the centre) vibrate separately. By making them both vibrate at the same time, it’s vidually confusing because reading from left to right, is expect you to have said “from the offset avd from the centre” instead of f“rom the centre and offset”. It’s a tiny detail, thought. Compliments again, great great great explanation

Also just one thing, I noticed a cut in the music at 16:54 but wasn't sure it was intentional or not.

Jonathan Fuzaro Alencar

Well that was brilliant. I just love it when you explain anything to do with physics, probably because I know far less physics than math.

Edan Maor

Loved the video! I think that the only mental-jumps still required are those that are prescribed by the "infinite intelligence" constraint :). One possible issue I did notice, although purely an animation thing, is the second fade-in of the (Radius)^2 term at around 13:58 - I just wasn't sure whether or not that was intentional.

Great, now I must postpone my sleep... thanks! :)

Jonathan Fuzaro Alencar

Dude this looks awesome! Can’t wait to check it out. Wish I could have had my name on it though.

this update is a blessing from the math gods