Projective geometry | Math History | NJ Wildberger

I love you Mr NJ WILDBERGER

As a graduate student specializing in Plato, this was a “wow” moment for me seeing the structure of reality where 2D/3D collapses down into 1D and that 2D/3D “project out of” a singlular “one” or point. Really beautiful to see mathematics and metaphysics really come together in this lecture. The drawing a picture metaphor was what made it click for me. Incredible stuff. Thank you professor.

YOU ARE THE SPIRIT OF MATH...GOD BLESS...

Amazing amazing

So cool 😎 What a wonderful lecture!!!

This is pretty good.

Great explanation

`712.a/?1st./[capitoal.L../nd.D

`712.a/?1st./[capitoal.L../nd.D

This lecture really infuriates me.I suggested to a young friend of mine who just did a Doctorate in physics and neurology that he should take a look at Projective Geometry to expand his researches.He told me tonight that he couldn't get a handel on it.I couldn't understand why he couldn't get it until I came across your mutilation of Geometrical Beauty.

Thank you so much for this! :)

Awesome. Thanks!

This has been very helpful... I'm watching this in 2022 still very fascinating thank you for this information keep up the good work.

Thank you for sharing this amazing lecture; very useful.

One of the most profound lectures of all time. The understanding of art, maths and perspective, extremely humbling.

Thankyou

is it weird that I'm just captivated by the coolness of this guy? the dude is just confident and well dressed and smart, and like a cocky cool guy.

You sir saved the day, i am currently studying computer vision and your examples made these ideas clearer to me. Have a nice day/(or night)

I feel like I gained a new perspective in my life. I can't thank you enough for this clear explanation of the topic Professor

I was reading a short story by Haruki Murakami where a character puzzled about "the circle with many centers and no circumference." I later thought it could be thought of as the line at infinity. Indeed, when I did a google search, I see results return about "the infinite sphere with center everywhere and circumference nowhere" which was a phrase attributed to Pascal. I'm more or less convinced that Pascal was talking about the line at infinity when he used that phrase. The non-orientability of projective plane puzzled me at first when I read it but the way you explained it makes it clear to me how the points at infinity loop around each other.

Good use of coloured chalk. Makes things a lot clearer than teachers who stick to one colour. Thank you.

This is excellent!

I am so enjoying this. 💕. Thankyou.

thank you sir

Congratulation Teacher. The lecture very good.

Thank you very much! This was quite easy to understand, and the thought experiment with the parabola was very helpful.

Awesome intro. Loved it! ❤

George Soros and the rothschilds are acceptable to Islam and the CIA Islam.

Thank you sir for such useful advice when captured by aliens

In France, MONGE projective geometry was taught up to 1985!...and then creepy idiots deciders of Mathematic High School programs, worked hard, following the US educational mediocrity, to destroy every year a little more the Maths teaching driving it to nowday NONSENS! In 20 years more then 60% of the insight has been thrown out of high school teaching, not only projective geometry, but almost all aspects of geometry. All planar and space insightfull geometric transformation that was taught has been erased, as crucial keys of calculus, ODE, vector spaces, group theory and even parametric curves including cinematic that was crasely trashed! It is a catastrophy for students that spring out of high school without almost knowing anything in Maths except some trivial little calculation carying no insight or deep helicopter view! It is an educational crime...

Severals coments shows that some confusions remain about "Euclidian Geometry" and "Relativistic Geometry". Make it clear in your mind that "Relativistic geometry" of (+ - - - ) signature, is AS "FLAT" (nul curvature) as "Euclidian Geometry" of signature (+; +++), and that in this regard, it is also "euclidian", in the sens of "euclidianaly flat". The only deep difference is that the "Relativistic metric" is not DEFINIT POSITIVE, which means that THERE EXIST NON ZERO VECTORS OF NEVERTHELESS NULL SPACE-TIME RELATIVISTIC LENGTH ! This has extremely paradoxal but extremely deep physical implication meaning that a light ray, in his proper time, arives in any place at the same time it is emmited !!! In other words it is "out of his own time,"...and so "IT IS" instead of "IT TRAVELS", as Shakespear puts it : "TO BE OR NOT TO BE"... Light rays definitally fall in the "I AM" category instead of the "I BECOME" one! Strange...but DEEP!

Thank you very much

Fascinating stuff! Keep up the good work Professor Wildberger! Really enjoy your videos.

We have gone down the rabbit hole, Dr Wildberger

This is AMAZING! Thank you so much for these, Sir!

I had 1 month of projective geometry in my linear algebra class

i have been an architect, a programming instructor that was interested in computer graphics, at no point in my career and education did i receive clear understanding of these topics, nobody understood proj geom, homogeneous coord, matrix transform, even perspective, ending up with rote dissemination and applications of these laws, equations and programs etc. In this very brief lecture, you managed to thoroughly illuminate me, so rather belatedly, kudos from a retired student！

1h 5m – Intersection of a non-circular cone with a sphere, can't be an actual ellipse, because a (non-circular) ellipse can't lie on a sphere and be planar.
It is, however, ellipse-like. Of course, if the cone is circular, the intersection is an ellipse, but one that is a circle.

lovely video and quite helpful for our teaching staff

very helpful!

very helpful!

good:!

Thank you very much ! This video is very useful !

Great video. Used the begining of it as an introduction to perpective drawing in a high school class going on a trip to Rome.

A reference for those of you who are interested in digging a bit more in this matter: N.J. Hitchin "Linear Geometry", Oxford 1987. Hitchin explains how the projective geometry can be considered using linear algebra (matrices and stuff). I used the paper for my Bachelors project back in 1992 :-)

Thank You You're Amazing!!! I'm a high schooler and I have a presentation tomorrow and you definitely saved me