sudgylacmoe | Two-Dimensional Lines Are Three-Dimensional - From Zero to Geo 1.9 Bonus Video @sudgylacmoe | Uploaded August 2023 | Updated October 2024, 1 minute ago.
This video is a bonus video in From Zero to Geo about the linear space of lines. This linear space has some interesting properties, and it is essential to PGA, one of the most useful flavors of geometric algebra. The title of the video is a bit of a joke, because lines are usually thought of as being one-dimensional, but we're working with lines in two-dimensional space, and their algebraic dimension is three using the approach shown in this video.

Sorry about the audio quality, this was actually recorded months ago with my old mic, and I didn't have time to rerecord it.

Here's the link I mentioned at the end of the video: youtube.com/watch?v=0i3ocLhbxJ4

This video is a part of "From Zero to Geo", a series where we formulate geometric algebra, an incredibly powerful branch of mathematics, from the ground up. Full playlist here: youtube.com/playlist?list=PLVuwZXwFua-0Ks3rRS4tIkswgUmDLqqRy
The previous video, mentioned at the beginning, is here: youtube.com/watch?v=If8r7vo4uoU

Discord: discord.gg/3Zj59zA2Rg

Patreon: patreon.com/sudgylacmoe

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Sections:
00:00 Introduction
00:44 How we write lines as vectors
01:22 Exploring the basis vectors
02:49 Adding lines (take 1)
05:05 Adding lines (take 2)
07:06 Magnitude
09:20 Conclusion