Відео

This is such a good video

Any idea if you can line integrate that curve to get the formula for the perimeter of an ellipse? Also this shows how "the jump from infinity to the next infinity is like the jump from zero to infinity" (zero rather than 1) makes some sense because in that diagram the zero to infinity line would continue from infinity to the next infinity in a straight line.

... this is so conceptually rich.. infinitely beautiful ..the horizon, the curve wrap at infinity, the perspective/projective dimension.... just amazing ..thnq

i didn't understand many parts of this. But enjoyed everything.

How does -2 times 3 is 5? In the cross raito part of the vid

you can tell he did this all in one take by the breath, what a legend

Can't you make delta = lim(d->0) d into an infinitessimal?

You should also make a video about axx + bx + c = 0 for a = 0, because that line now also has two intersections if you perceive a as an infinitessimal.

I'm following your playlist. I've arrived here but feel like I missed a video or two. The start of this video seems to assume that I can now differentiate trig functions and log functions, but I didn't see a video in this list that covered those beasties.

I finally understand the Chain Rule. Many thanks!

The fact that Parabolas are just ellipses stretched to infinity may not be as a surprise if we remember about the conic sections. Circles are when the plane cutting it is paralel to the base. Ellipses are when they are oblique, but not parallel to the side, and parabolas are when the plane is parallel to the side of the cone, so it is the first ellipse that "couldn't find" the other plane to close on itself. Hyperbolas are when the plane is orthogonal to the base. I didn't know hyperbolas were parabolas in projective geommetry, but it makes sense, since they are orthogonal, they would only be a parabola in the extreme case where the angle of the cone is orthogonal, but in that case it wouldn't be a cone, but a cylinder(in which, in projective geommetry, it would be a cone at infinity). Pretty cool!

It looks like the Bézout's theorem and the fundamental theorem of algebra are equivalent. If you carefully define an operation that "adds" two implicit curves together, it should transform one to the other.

I always thought about how to properly prove the foci of a parabola (for orbital mechanic purposes). I know the equation, it is simple, but I just couldn't get my head around the "other foci being at the infinite point". This video has showed me how that works and I feel GREAT now. Thanks!

Wtf did i just see

So you looked up from the ground?

You must have a phd in yapping 😂😂

New and exciting ways to confuse flat earthers.

This was strange. Just 20 minutes ago, I was imagining making a video where a curve that looks like a parabola up close is actually an ellipse when you zoom out. And then I get recommended this!

Great video!

Came for the graphics, stayed for the graphics I feel like I just wasted a little over 10 minutes on math I didn't bother to understand... Of course it's totally a me problem but I still feel a bit miffed about it :P I wonder what happens if you make the lines stop being parallel and slowly converge at some point but never quite touch That probably sounds silly when you think about it but I want to experiment with it

But perspective doesn't turn parallel lines into intersecting lines, it turns them into curves...

like how you used your own music for the intro

9:37 I bet this is related to the fact that gravity draws parabolas (at our scale) but also elipses (at very big scales).

Excellent.

I don't understand a thing of what this video said. But it reminds me of when I heard that anything is possible at infinity.

Just wow.

18:44 THE SIXTH DIMENSION????????

The Fermat’s Last Theorem cameo hit me like a ton of bricks

🙏🙏👍👍

Moar

Fantastic video.

dang it, now I have to deal with another fundamental theorem too?

6:40 wouldn't it be more accurate to say that bd/ad≈b/a which in fact can be very far from 1 Edit: nvm I'm dumb

Very good video

👏🏻👏🏻👏🏻👏🏻

This helped me find where to look for more information about the point at infinity. Thank you!

11:11 YES. finally someone said it -∞ and +∞ are the *same*. everything works the same at that. one graph that shows this very well is y=1/x, where both go to ∞. it looks like different directions, but really the number line just loops at infinity.

This video has made so many things so much clearer to me.

10:02 At last, I understand homogeneous coordinates

If a parabola can be viewed as an ellipse through perspective, how does the directrix come into play here, I’m interpreting this as meaning that ellipses have their own equivalent of a directrix, and by extension, the rest of the conic sections do as-well.

18:44 chatgpt said a complex projective plane can be represented in a 4d real manifold, not 6d, is this correct?

Mind opening! Well done 🙏

Wow!

26:36 you mean, once you circle the last number that is less than the square root...

Beautiful Explanation!! You deserve an oscar👌👌👌👌👌

1:18 1:14

Hi Bill! A question: Where did the "1.5" factor for the outliers estimation come from?

Excellent!👌

thank you so much for posting these, you teach so well! so concise yet nothing important is left out. I tried so hard to learn thru just reading the textbook and it seemed impossible. but one video of yours made it seem so easy!