I have some references in the description, but only the first two (the Wikipedia article and Wildberger's video) are specifically about projective geometry, and none use the same notation as this video (they use homogenous coordinates, whereas I just use vectors). I also recommend knowing a bit of linear algebra.

just cache friendly code

True, the second half of the video was heavier on linear algebra and a way of manipulating matrices that might not be very well known, but I hope the first few minutes where I define projective points and lines were understandable and showed where projective geometry could have arisen from.

Thanks! I notice that on your about page you have a link to a Desmos page showing perspective projection of a parabola. www.desmos.com/calculator/5kalh6a9b3

@@coolcomputery Yup, that was a response to one of the comments on the Bill Shillito video

Hello, I'm sorry to say that I won't be active for a while, and if I make another video it will most likely be unrelated to geometry (I am busy with college and two research projects at the moment). I will say, however, that affine transformations in a n-dimensional space are equivalent to linear transformations in (n+1)-dimensional space that preserve some n-dimensional hyperplane that does not pass through the origin. For example, the affine transformation (x,y) --> (ax+by+e,cx+dy+f) that transforms the points (x,y) in 2D space can be turned into the linear transformation (x,y,z) --> (ax+by+ez,cx+dy+fz,z) that transforms the points (x,y,1) in the z=1 plane within 3D space. Theoretically, affine geometry could be formulated as a restricted version of linear algebra. Hope that helps!

@@coolcomputery Wow, very informative; thank you so much for this little help, man !!!!! Though I’d only just recommend that you use the symbol “|-->” for symbolizing (the action of) your function, when you’re describing it in terms of the general (set theoretical) form of your 3-tuplets; at least in the future Also, another question : Whenever you used, such as (if that wasn’t the only time this _actually_ occurred as I described it) @…, as many rows in your vectors as there were dimensions in your vector space using them, well, since of course you can actually have many wildly more diversely “n-valued” n-tuplets that can be part of a vector space of a constant (i.e. definitely NOT ALWAYS “n-valued”, as opposed to what may imply its elements of theirs) dimensionality, I was wondering if it wasn’t actually that you were implicitly using some sort of “canon” or “ultimately simplified numeric & symbolic representation of the mathematical ideal of the vector space in question”, where you “reduce”, or “ _’extract’_ all of the _’redundant’_ _’numbers’_ & _’distances’_ between them”, or smth; It especially hit me in how it looked like what basically boils down to, as far as I’ve actually read into the subject/topic, how a so-called “lossless image file data compression algorithm” would basically reduce the amount of information initially needed/procured by the initial file to properly record a certain pixel’s state (which’d also be structured computationally & logistically as an n-tuplet containing all the quantified properties as values arranged inside each of the “n” “slots” of that “tuplet” : The algorithm would, like, essentially reduce the cardinality of what’s essentilly just a family - i.e. “vector” or “tuplet”; or, again, it’d just lower the value of the “n” -, as well as just “bring all the numbers closer together”, with all the numbers - that are both/either possible &/or actually present in the currently processed/compressed file - occupying as little space inside the memory as possible)

Thank you! It has already been submitted.

Thanks for notifying me about the corrupted links: I indeed have a master version of the video description and have just copy-pasted it again onto KZbin; the links still display '...' but they are working now (as of writing this comment). I could produce several smaller videos, but I wanted to create a single self-contained video that covered the entire process of formulating projective geometry, so that anyone who watches this video could potentially use it for any possible applications of geometry (e.g. making a 3D engine). Plus, one video is (in my opinion) usually more convenient than several smaller videos (even in a playlist), and I'm not sure if #SoME2 allows a playlist of multiple videos to be an entry. Lastly, my next few planned videos (if I manage to make them) will be on completely different topics in math. I'll be sure to look more into Wildberger's rational trigonometry and chromogeometry!

sudgylacmoe just released a very good introductory video on Projective Geometric Algebra :) kzbin.info/www/bejne/ZpqWoJaCncergJY > the antiwedge product, which performs an operation analogous to the intersection use here In regular PGA, the meet of two lines is just their wedge product. It's not clear for me what Lengyel's formulation brings to the picture.