@AllenKnutson Don't give me that "I'm not sure how to do a 6×6 determinant" jazz. I know for a fact that you can do 8×8. (Granted, the matrix was at least half zeroes, if memory serves, and evaluated to 8 factorial, but still impressive.)
@@tomkerruish2982 That wasn't the lie for the video that I had the most trouble mouthing. It was "I thought the complex plane was the same as the real plane" 26:32 . Yuck. Taran carried off the subsequent sigh very well I think.
@@AllenKnutson I listened to it again. That was a very good, heartfelt sigh. Another good piece of acting was when you feigned incredulity about being able to just change the rules in math. Heck, I'm pretty much a Platonist, and even I say that's how you go on a journey of exploration and discovery.
Honestly one of the greatest math videos I've ever seen, everything is explained really clearly in a novel and very effective format. And its real math not over simplified pop math. Please make more videos! This was amazing!
@@AllenKnutson Honestly one of my only problems with this video are that the subtitles are confusing in some parts. I had to re-watch parts of the video more than 5 times to figure out who exactly is saying what. Just using "A" and "T" to distinguish who's saying what doesn't really work very well. You can actually color RU-vid subtitles, (I don't know how, though. I've only ever seen it on Tom Scott's videos, so I'd ask him how exactly he does it) so I'd suggest using that rather than your current way of, distinguishing who's speaking.
There's actually a lot of tricks available in this format. E.g. Taran can make some advanced/esoteric point, which in a one-voice video might run the danger of derailing the main thread, and I can go "WhatEVER" and bring the focus back to the central story.
Computer vision algorithms tend to work in RP3. It was fun seeing how the some of the concepts used there can be visualized. I really enjoyed the animations of the antipodal spots and great circles on the sphere.
This gave me flashbacks to the distant past, when I used to work on elliptic curves. I think I spent a week or so making graphs of projective elliptic and hyperelliptic curves. It was definitely a week well spent.
Unbelievable video, thanks. As someone with a maths background who is a bit embarrassed I never learned any projective geometry this was really clear and interesting.
I love the dialogue format that is taken in this video! It’s very intuitive and answers many questions which a viewer might have while also being extremely engaging
Like everyone else here, I'm rating this 10/10. This is the most accessible video I've come across on algebraic and projective geometry. Sadly I'm only an engineer and lack so much mathematical foundation, but this refreshing and intuitive explanation will certainly help me I'm my research :)
This video was fucking illuminating for me, i studied projective space in geometry and i didn't have the right imagine of how to think the projective space or projective conics, thank you very much
Very underrated project. It's a really amazing way to teach students about these topic that are generally difficult for them to grasp at first. Well done
Well hells bells, lads. I understand things now that I didn't understand before by watching this video. Super neat. I'm absolutely going to watch this again with the hopes that it'll happen again.
Wow this is really incredible!! and I totally buy and approve all the comparisons with Outside In (of which I was one of the creators..) great explanations of deep math. love it.
This video is amazing! I have yet to learn anything about projective/algebraic geometry, and this video got me hooked immediately and completely blew my mind. This is just beautiful mathematics. I also really like the format of the video as a dialogue, it is very relaxing in a sense. Can't wait for this video to blow up
This was wayyy up there in terms of mathematics video quality. I just had my second semester mathematics exams. Already looking forward to geometry in the 4th semester. I am seeing a lot of similarities between the snippets from what my friend told me about that course (largely focused on hyperbolic, spherical, / just non Euclidian geometry) and this video.
this is a gem, though I do get lost at a few points: 1. 6:37 why there's "got to be" a point passing through itself three times 2. 16:48 the space of answers for exactly what? Curves passing through serveral points, lines tangent to several curves and etc?
1. This is definitely not supposed to be obvious. It can be proven but it's not important for this video 2. The number of conics through five points in particular, but also the space of lines that go through two distinct given points _and_ the space of points that lie on two distinct lines _and_ the space of lines tangent to two circles are all zero-dimensional. Thanks!
This is a very well-done video! Two notes: - You introduced the p_m notation near the start, but never brought it up again. Is this the same as [1,m,0]? In this case, the two points on every circle are p_i and p_-i. - I second the comment someone else made that you should see if you can color-code the subtitles.
The circle thing makes sense given that every scaling and translation of the hyperbola x^2-y^2=1 contains the points p_1 and p_-1. Circles are scalings and translations of the equation x^2-(iy)^2=1.
While I definitely saw Outside In nigh 30 years ago ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-wO61D9x6lNY.html I had completely forgotten that it is done as a dialogue. We were more inspired by the flow of actual conversations (between the two of us, and with other people), as I'm sure the Outside In people were.
It's just a name. We're not going to do algebra with it, e.g. try to "multiply" two slopes together. You're worried that you got a hold of the slope as a/b, and in other contexts it's safer to say "that ratio is undefined" than to say "that ratio is infinity". In _this_ context, the reason that people like "infinity" as the name for the vertical slope is that it suggests the right "topology on the space of slopes". Concretely, you should think that just as if we consider lines with slopes 5.1, 5.01, 5.001, ... we'll sneak up on a line with slope 5, if we consider lines with slopes 10, 100, 1000, ... we'll sneak up on a line with slope infinity.
The traditional quadratic formula applies to quadratic equations in one variable. If we were looking at a general quadratic equation in two variables ax^2 + bxy + cy^2 + dx + ey + f = 0, there'd be no way to factor it. But in the case at 24:20, the equation is the homogenization of a quadratic equation in one variable, so the traditional quadratic formula can be applied.
Hmm, I'm not sure how to explain this in another way. The green line has some slope m, and by definition this means that it has the point p_m on it. The purple line is parallel, so it has the same slope, and therefore also has p_m on it. They share the point p_m in the same way that non-parallel lines share their intersection point.
