Euclidean & Non-Euclidean Geometries Part 5: Axioms (Cont.)

[edgeArchitect]

About parallels:

What if a point P is not fixed, but is at Infinity?

[animimm]

In fact the uniqueness of the circle is included in the definition of a circle, as the def says it is "the set of ALL points.." :)

Thnx for the videos :)

[Prepoceros]

I get the sense that your videos are making almost the same point as my "proving theories" video, but with more rigor and less hand-waving. =) Looking forward to the conclusion!

[DarwinsHamster]

I did post my first video in the series as a response to yours, and in the meantime have used your name in response to other comments and explicitly noted the connection to your video in the expanded description to Part 1 and a longer comment I made on my channel page yesterday in response to a comment there.

[Prepoceros]

Ah, so you did. I hadn't noticed the comment.

Watching is my pleasure. =)

[DarwinsHamster]

There's no way you could have noticed the comments unless you monitored them over time because I change the video descriptions over time and the comments of others followed your viewing of the videos. Thanks again.

[DarwinsHamster]

I will be doing some hand-waving, but hope to make the disconnect between "reality" and mathematics as dramatic as possible. I hope to be able to ask for your help after the last formal video if there are questions from viewers that I can't deal with. Thanks for watching.

[shaynexus]

Bravo. But nowhere have you made the point that all the lines are or are not on a single plane.

Dennis

[DarwinsHamster]

I certainly neglected it way, way too long, but I think I finally said something near the end. I am going to go back and put that clarificantion in the comments for Part 1, and maybe even make a Part 0 to explain your point and to clarify that this all isn't ultimately about geometry, but some other mysterious point I want to eventually make about proofs of theorems vs proofs of theories.

[ashboxtoo]

LOL Good video, I read your pre warning of the candle holder at around the same moment it happened. Made me crack up laughing.

Again great stuff, very educational for me to listen to your explanations about this stuff. Thanks again.