Euclidean & Non-Euclidean Geometries Part 1

This is a series of videos ostensibly about geometry; however, if you don't already know some geometry, you're unlikely to learn it here. The series was inspired by Prepoceros' video about differences between proving theories and theorems and some mind-boggling (to me) points I learned from a non-Euclidean geometry course many years ago.

I am going to emphasize the roles of definitions and axions way way more than one might think necessary, considering that I am already assuming some knowledge on the part of the listeners. Trust me.

Although I don't say so until Part 5, this is about plane geometry unless I explicity say otherwise, which I haven't done at least through Part 5.

Don't look for any elegant proofs in these videos.

The book that I am borrowing ideas, anecdotes and other stuff from is:

Euclidean and Non-Euclidean Geometries: Development and History, Second Edition, by Marvin Jay Greenberg, published by W.H. Freeman and Company. Although it is not obvious, there is more than geometry to this book, and it is worth searching for.

Category:

Howto & Style

Tags:

• prepoceros
• websnarf
• theory
• theorem
• proof
• science
• math
• mathematics
• geometry
• epistemology

[swaineadeney]

How can you teach a "non" without a concept of the true?

Euclidean Geometry is beautifully logical, impeccably linear.

It's rather like saying, "let's teach our children abstract theories of existence before they have any real experience of having lived and reflected on those experiences"

[DarwinsHamster]

I think I pretty much agree with you.

[gorilla55215]

am i the only one who feels like this guy doesn't really have a legitimate background? i think he just reads up on stuff on the internet and studies it before he decides to make a video because i was watching some of his "science" videos and he said he was an undergraduate physics student. now he's a damn lawyer? what the hell. idk but i think this guy is playing a lot of ppl.

[DarwinsHamster]

Not only that, but I was a professional musician (violinist) and have played on stage with Sammy David, Jr., Andy Williams, Perry Como, Dinah Shore and maybe a few others I can't think of.

Plus I now work as a database troubleshooter for one of the largest software companies in the world.

Kind of makes your head spin, doesn't it?

[brukernavn1]

We "teach" both spherical geometry and topology in preschool. It's not hard, nor is it really something new. Kids experience both every day. All that's missing is someone to put their experiences into the right terms, i.e. a ball is a ball because it's a sphere. If we take the air out of the ball, is it still a ball? can it do the things a ball does? It's still topologically equivalent to the spherical ball, but yet it's somehow changed. Suddenly you're not teaching maths any more but philosophy

[ARGYAmphetamine]

I turned it off after 2:30.

I didn't need to hear this guys life story.

[ix8880]

@gorilla55215 You've never heard of a polymath? Some people enjoy learning and doing stuff more than maximizing their income by sticking with one thing and just milking it until they drop dead.

[FallofDarkness55]

string theory. 

[StrikaAmaru]

@AnonymousWhitePerson "Euclidean Geometry is based on unproven A Priori Axioms"... so is Riemannian geometry; it's just that the fifth postulate of Riemannian is the negation of Euclid's fifth postulate. You know, the one with the parallels?

"and is premised on a faulty assumption that the shape of the Universe is Flat" It's premised on the assumption of a non-changing curvature. If you want to sound educated, at least use the proper lingo.

[StrikaAmaru]

@AnonymousWhitePerson Correct me if I'm wrong, but Riemann's geometry started out as a thought experiment: what happens if the fifth postulate is turned on its head? The answer: an entirely different, entirely consistent geometry. It wasn't until Einstein's relativity that we demonstrated space is on the large scale not-flat and the geometry of the Universe is Riemannian.

BUT on the local, small scale region, Euclidean geometry works just fine.

[GenghisTaam]

you could also call Euclidean geometry non-hyperbolic Geometry and say the same thing. the idea that Euclidean geometry is the intrinsic structure of physical space, and that any other geometry is "only an abstract theory" is exactly the kind of mistake corrected in Greenberg's book.

[GenghisTaam]

you could also call Euclidean geometry non-hyperbolic geometry and say the same thing. assuming Euclidean geometry is the intrinsic structure of the physical world, and that any other geometry is "only an abstract theory" is exactly the mistake corrected in Greenberg's book.

[Grim4566]

@GreatCommunistEmpire

Ohh that's right you don't get to watch TV in communist China in communist China TV watches you.

Obviously Harry refers to Harry Houdini - Greatest Welsh Born Film Director

Obviously Sally refers to Sally Jessy Raphael - greatest person to fight of the communists in cold war Russia circa 1985 when America invaded Pingluo, Communist China, to destroy the massive opium trade that was ripping apart cities across the globe. It was a treacherous task.