Projective geometry | Math History | NJ Wildberger

[@YAUWAI8008]

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！

[@4DMovie]

I taught myself descriptive geometry with only an innate understanding of projective geometry.

[@DrTWG]

@@4DMovie You are a very clever boy then . You can have a badge.

[@surajmandal_567]

A student is never retired 😂. Just Joking

[@jonathanfanning9558]

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

[@njwildberger]

In the 19th century it slowly became clearer that most other geometries (Euclidean, spherical, hyperbolic, inversive) can be built from projective geometry. It is also the main framework for modern algebraic geometry, which grew out of it.

[@owen7185]

It's amazing

[@helioliskfire5954]

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.

[@njwildberger]

@EmanT777 Yes projective geometry is indeed a unifying framework for other geometries. This is not properly appreciated these days, one of the reasons students often miss out on this important geometry. Projective geometry and Mobius geometry are also closely related. I will discuss such topics in my Universal Hyperbolic Geometry series.

[@njwildberger]

@madier1000 You might like to know that in my WildTrig series there is a 8-10 part segment on projective geometry, if you are particularly interested in that topic.

[@ChristinaPhillipsartist]

Thank you, thank you, thank you Prof. Wildberger for thinking to put these videos up. I am revising after many years out for a CS PhD studying impossible objects. I need a deep understanding of topology and projective geometry and your lecture series is a fantastic start.

[@4DMovie]

The study of imposable objects must start with a read of "Fundamentals of Three-Dimensional Descriptive Geometry" and "Four-Dimensional Descriptive Geometry" by Steve M. Slaby and C. Ernesto S. Lindgren.

[@anderskristoffersen3270]

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 :-)

[@yuxiao8544]

Thank you sir for such useful advice when captured by aliens

[@kebakent]

I'm reading Multiple View Geometry in Computer Vision, and this was very helpful. Thanks!

[@rah1721]

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

[@imrematajz1624]

at 37:37 the fuse is carefully lit and it blows my mind by the end of Professor Wildberger's lecture...just a hyperbola, so to speak😮❤

[@alavifazel]

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

[@heruilin]

Excellent lecture. I especially admire your ability to accurately diagram on black board.

[@panagiotiskarampi3851]

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)

[@water0heaven]

Epic! This video should be the first ingredients for persons like me, who have never come across projective planes before. Nice work!

[@IronHuge]

The alien metaphor is so great, it makes me very happy! Thank you.

[@Jekku1987]

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

[@njwildberger]

Thanks!

[@lindapatan]

We have gone down the rabbit hole, Dr Wildberger

[@madier1000]

I enjoyed this lecture very much and look forward to the whole serie.

[@AlgebricDiddle]

Thanks to you I'm learning something interesting while improving my English listening.

[@Igdrazil]

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...

[@4DMovie]

This is not taught in the USA! C. Ernesto S. Lindgren was recently named the #ModernGaspardMonge.

[@sahithkumaryedakula185]

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

[@DavidZimbeck]

this guy is an amazing teacher!!

[@murthy1023]

Great explanation

[@OldSportDispatch]

Awesome. Thanks!

[@vivaviiv]

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

[@njwildberger]

Two points at infinity are connected by the line at infinity. This is the one line we need to add to the existing line to go from the affine to the projective plane. As for the WildTrig series of videos on Rational Trigonometry, that is 21st century mathematics all the way! But still with its origins in the work and thinking of the ancient Greeks.

[@magnamia]

Thank you so much for this! :)

[@noormuhammadmalik6191]

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

[@brendawilliams8062]

I am so enjoying this. 💕. Thankyou.

[@ME-yp7fn]

Excellent lecture, thank you so much

[@antonellomascarello4698]

So cool 😎 What a wonderful lecture!!!

[@PatrickPease]

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.

[@ashishjain871]

Thank you for sharing this amazing lecture; very useful.

[@ShahryarKhan-KHANSOLO-]

Awesome intro. Loved it! ❤

[@peterhi503]

Excellent, Wildberger. At 45', it might be slightly better to assert P = R union, not R plus, infinity.

[@PhilBailey]

I love his style. Very easy to follow. I subscribed and will follow lectures as I'm finishing up my BFA. Thank you Sir.

[@rivers64]

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

[@panchodayasecondaryschool5698]

lovely video and quite helpful for our teaching staff

[@njwildberger]

Hi 172Break If you have a lot of maths ability, you might consider that. A warning however: in many maths departments, doing a PhD is not so much about learning a lot of interesting mathematics in a wide area, but rather learning a lot of less interesting mathematics in a narrow area. This is an unfortunate consequence of socio-economic pressures in the system. There are advantages in being an amateur!

[@maxwang2537]

This is a great point and I totally agree. This might be somehow irrelevant but I’m a strong disbeliever of the idea of making your hobby and your profession one-to me, that way, the pressure to make a living from it or, in broader terms, the social-economic pressure can too often and too easily ruin your joy of doing it. I have a similar background with a masters in engineering and a love of mathematics so, not very surprisingly, once also had the same dream of doing a pure mathematics degree (it does not have to be PhD) regardless of age. Now I tend to believe doing it as an amateur is a better idea, particularly so because we now live in an age of knowledge democracy, with such wonderful stuff from channels like this readily available. Also, if I can ever manage to finish all the lectures in this channel (fingers crossed) with, say, an 80% of rate of comprehension, I would happily print out and issue myself a certificate of an honorary PhD in pure mathematics and frame and hang it on the wall of my study!

[@Dooyc]

Thank you very much ! This video is very useful !

[@josemarcelo2882]

Congratulation Teacher. The lecture very good.

[@njwildberger]

I'm glad you like it.

[@njwildberger]

Hi peterhi503 Perhaps, but I am not a big fan of `infinite sets' so I try to steer away from the notation associated with that topic.

[@njwildberger]

Hi 172Break This year there will be 12. But next year I hope to add some more.

[@jamie64ful]

thanks for the videos, very helpful. where did this lecture take place?

[@mashmax98]

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

[@njwildberger]

Thanks!

[@ethanjensen7967]

This is excellent!

[@陳志源-f9y]

Thank you for this lesson! It's really helpful and you presented it so well! I do really appreciate it! I found CG community use 4x4 matrix to do affine transformation, but few teachers do explain the reason this specifically. I watched this video whole day and take my note with some pictures I made in Rhino. Here's the note: drive.google.com/file/d/1svSKEk4jApfo_x35fO5H6CffYzVeRUDE/view?usp=sharing Thank you to make this quality lecture!! THANKS

[@njwildberger]

Thanks for the nice comment. You put unite a lot of work into the Notes you made, and they look great! Well done. If you don’t mind, perhaps I could link to your notes in the video description? That way other viewers can also benefit. If OK, please also give me your (English) name so I can attribute.

[@陳志源-f9y]

@@njwildberger Thanks!! My name is Jim Yuan.

[@njwildberger]

@@陳志源-f9y Thanks Jim, I have now posted the link to your notes in the video description.

[@ffggddss]

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.

[@Professeur-Nazaire]

Wondering about that. The 3d points (0,1,0) and (0,0,1) are on that ellipse/circle, regardless if the original parabola is y=x^2 or y=m x^2 for some positive m. Changing m should change the ellipse but cannot change the circle. I guess it is an "ellipse-like" think on the sphere. Norman?!

[@indus7841]

This is pretty good.

[@AllYourMemeAreBelongToUs]

38:50 Fascinating

[@roonyroony7365]

Thank you very much

[@ni3cat]

Amazing amazing

[@zulkarnainsina5175]

thank you sir

[@Igdrazil]

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!

[@pedropfaff8906]

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.

[@pedropfaff8906]

Excectly how stupid are you that you are completely oblivious that you are butchering the beauty of Projective Geometry.

[@robertgilmore1655]

Thank you!

[@TheLyue]

very helpful!

[@dysonsphere3005]

Thank u for the video

[@brendawilliams8062]

Thankyou

[@mauricioveron8116]

good:!

[@TheLyue]

very helpful!