Introduction to Projective Geometry via Tic-Tac-Toe Grids

My entry for @3blue1brown's Summer of Math Exposition 2022.

It's my first video ever and there are a million things I would like to improve. Mostly the audio quality and my terrible, terrible accent. 😅
Alas, perfect is the enemy of the good, isn't it. So, here we go.

#SoME2

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Animations were made with CindyJS:

For more information on Projective Geometry, I recommend the book Perspectives in Projective Geometry by Jürgen Richter-Gebert:

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Chapters:
[00:00] Opening
[00:40] Introduction
[01:48] Projective Transformations
[04:10] Incidence Construction
[06:55] The Cross-Ratio
[16:33] The “School” Method
[19:33] Epilogue

[johnchessant]

Very nice! The cross-ratio is one of my favorite less well-known topics. With the Mobius transformation view, we can see that the cross-ratio of four complex numbers is real if and only if they lie on the same line or circle.

[pos_itronium]

when i was younger, every time i tried to get some bit of projective geometry, it was just a mysterious mess to me. well, maybe, i could remember something, do formulas, make some constructions, but the essence was still unaccessible. now, when some maths intuition settled in my head, i am starting to rediscover a lot of mathematical concepts, so videos like this are very useful not for getting some rigid knowledge (you may always read a textbook or a Wiki page for this purpose) but learn some motivation of a concept, get the intuition, highlight the connections with other math stuff and well, really understand what's going on. so i'd like to thank a lot the author for the video, it really uncovered some bits of information needed to order my previous knowledge.

thank you and good luck in developing the channel!

[antonseoane]

Really nice video. I've just made my final bachelors degree project about projective geometry and used de cross-ratio (which i knew as double ratio) to make an euclidean clasification of the conics.

[BharmaArc]

I'm really happy you decided to share this video as it was very clearly presented, well animated and well paced. Love the subject and how you made it easy to follow your train of thought by using (wonderful) animations. Great job!!

[ayrapetoff]

Both explanation and visualization are just perfect. Thank you!

[thatisjake]

Shocked me when this channel only had 1k subs. This is a gold mine. Keep it up!

[kasugaryuichi]

This was a pretty fun watch, thank you <3

[gameswoodmore]

Great Video! The way of looking at the harmonic construction as a projective parallelogram was really nice, I wish we would have been shown that in our geometry lecture!

[erikzdrumpi]

BEAUTIFUL! I can finally get a proper introduction to projection geometry without the need to look up all different books on the internet! Nice!

[gunjanlakhlani]

Very good exposition. Really really clear, I thoroughly enjoyed it!

[llblumire]

The mathematics, explanations, and animations are beautiful, but the background music is too loud and drowns out your voice for me :(

[ukor]

Really, really nice! And what a great starter for any lecture about Projective Geometry. If all maths and maths ed students just knew what you showed in the video, the world would be a better one!

[thebees]

This was absolutely fascinating - great job!

[AnakinSkywalker-zqlm]

The channel looks brand new. Best of luck. It’s gonna grow! Mark my words

[Macgki]

I was considering doing a video entry on projective geometry after listening to Prof. Richter Geberts great lecture, I but scrapped it due to time issues. What a coincidendce now to see you make this wonderful entry :)

[stephanejaouen]

thanks ; very interesting (sehr angenehm :) )

[ayrapetoff]

3:13 This moment is brilliant and enlightening

[christophertinklerart]

Please do more videos, your explanations are very clear, great job

[JohnDlugosz]

I recall from a drafting & architecture class in high school that the formula for measuring along the axis in perspective was something simple involving the cosine function. I suppose that was an approximation.
When I took computer graphics in college, I recall the extra dimension allowing perspective transformations, and that moving a parameter changed the perspective; but I don't recall any formula for how that relates to the vanishing point.

[premsinghpoonmagar]

This video came as an suggestion. It's a good video for understanding, as I find it's your first video.. I am hoping you do more of this🥳 love from Nepal 🇳🇵