sudgylacmoe | What is (a) Space? From Zero to Geo 1.5 @sudgylacmoe | Uploaded December 2021 | Updated October 2024, 2 hours ago.
What is space? In this video, we learn about the many different things that we might call "space". We come up with both a geometric and an algebraic definition, and the discussion also leads us to the important concept of subspaces.
Sorry for how long this video took to make! I mentioned in a community post that I had personal things interfering with making this video, but even after that was out of the way, this video was really hard to make. I kept rewriting parts of it to be less confusing, and a few changes I made required drastic modifications to whole video (for example, I was originally going to define linear combinations here but then decided to wait until the next video, but I had used linear combinations in the rest of this video so I had to remove all references to them). Hopefully the video is worth the wait.
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
Next video here: youtube.com/watch?v=uByHD38Xsls
Discord: discord.gg/3Zj59zA2Rg
Patreon: patreon.com/sudgylacmoe
Patreon Supporters:
AxisAngles
Couspar
Richard Penner
Sections:
00:00 Introduction
01:05 Describing regions with vectors
01:52 What is space?
03:24 Geometric definition of a space
04:40 Algebraic definition of a space
08:41 Basic consequences of the definition
09:32 Subspaces
10:13 Line exercises
11:54 Half-plane exercise
12:32 Scalar multiple exercise
14:21 Unit vector exercise
14:43 Zero vector exercise
15:35 Subspaces of all spaces
16:03 Classifying all spaces
16:43 Conclusion
What is space? In this video, we learn about the many different things that we might call "space". We come up with both a geometric and an algebraic definition, and the discussion also leads us to the important concept of subspaces.
Sorry for how long this video took to make! I mentioned in a community post that I had personal things interfering with making this video, but even after that was out of the way, this video was really hard to make. I kept rewriting parts of it to be less confusing, and a few changes I made required drastic modifications to whole video (for example, I was originally going to define linear combinations here but then decided to wait until the next video, but I had used linear combinations in the rest of this video so I had to remove all references to them). Hopefully the video is worth the wait.
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
Next video here: youtube.com/watch?v=uByHD38Xsls
Discord: discord.gg/3Zj59zA2Rg
Patreon: patreon.com/sudgylacmoe
Patreon Supporters:
AxisAngles
Couspar
Richard Penner
Sections:
00:00 Introduction
01:05 Describing regions with vectors
01:52 What is space?
03:24 Geometric definition of a space
04:40 Algebraic definition of a space
08:41 Basic consequences of the definition
09:32 Subspaces
10:13 Line exercises
11:54 Half-plane exercise
12:32 Scalar multiple exercise
14:21 Unit vector exercise
14:43 Zero vector exercise
15:35 Subspaces of all spaces
16:03 Classifying all spaces
16:43 Conclusion
