Every Level of Geometry Explained

Рет қаралды 33,019

ThoughtThrill

Күн бұрын

Пікірлер: 53

@iteo7349 Ай бұрын

This video is like a Chat GPT answer.

@thelightningwave Ай бұрын

You pretty much summed up the channel's content.

@thisguyisnotable Ай бұрын

the voice sounds like AI too

@m_c_8656 13 күн бұрын

A disc (or disk) is defined as the region within a circle. A circle is the set of all points in R^2 that are equidistant from a fixed point known as the center. A circumference is the length of a circle.

@chessematics Ай бұрын

The amount of misinformation confounded me

@marcelob.5300 Ай бұрын

Please elaborate and provide additional details.

@iteo7349 Ай бұрын

@@marcelob.5300 Let's take just the sentence "The best known algebraic surfaces are surfaces of order 2 or quadric surfaces" as an example. First, why specifically surfaces (dimension 2)? There are also curves (dimension 1), and higher dimensional things (dimension >=3). Second, nobody calls it "order 2", it is called degree 2. Bonus: A few second later "order" (degree) is defined in two ways, both are correct only for surfaces embedded in P^3 (3-dimensional projective space), in general the first one is not well-defined, the second one is false. Third, when you say quadrics are the best known surfaces you'd imagine there are a whole lot of these "quadrics", right? Guess how many there are. One. It must be the product of two projective lines, that's the only one. (At least with the usual implicit assumptions that the surface is smooth, projective, and defined over an algebraically closed field. Or if you don't make those standard assumption, then no way you can call what you have in mind the "best known algebraic surfaces".) Finally, the statement itself that the best known surfaces are the quadrics is a bit like saying that sin^2(x) is the best known function in trigonometry. Anyway, I'm not hating. The video is nice to watch and I had fun, but it's fair to say it's just for fun ... not extremely accurate.

@lyrimetacurl0 Ай бұрын

@@iteo7349 thanks for this forewarning :)

@anaisnintuition Ай бұрын

I wanna know what you mean by this as someone who doesn't understand the video

@QuaziAymanUzayr Ай бұрын

The equation at 5:00 is also wrong 😂. It should be just y-y1=m(x-x1)

@jsalsman Ай бұрын

There are multiple errors and misconstruals in this video, unlike the others in this series.

@solar_aintdead4270 Ай бұрын

Yeah I thought that point-slope formula was y-y1=m(x-x1) not with the +b

@MathSenseiYT Ай бұрын

@@solar_aintdead4270 I think that it was meant to be like slope intercept when calculating an equation. I could be wrong though.

@xinpingdonohoe3978 7 күн бұрын

f(z)=√x is an odd one.

@SoliceLilith 6 күн бұрын

It’s 5 in the morning, English is not my first language and in school I hated geometry and always preferred algebra. WHY ON EARTH IT IS THE SECOND VIDEO FROM THIS CHANNEL THAT I WATCH?

@pseudoexpertise Ай бұрын

Very weird take to say that in between topological, non-euclidean, algebraic, analytical and differential, one is more advanced than the other. They just answer different questions: Topological geometry can look at geometric properties of spaces that do not even have angles or perhaps not even magnitudes or distances at all. Algebraic geometry, well, focuses on the algebraic properties of points surfaces and other manifolds like finding rational points on elliptic curves or proving that one curve is trancendental. Differential geometry cares about questions involving time and motion. So next to finding shortest path they ask for the fastest way too. And these two can be two different solutions. None is more advanced than the other. These are separate areas that are working on different problems.

@pseudoexpertise Ай бұрын

... at least as far as I'm concerned. Don't cite me as a source or sth.

@xinpingdonohoe3978 7 күн бұрын

I haven't done them all, so I must ask: are they all as technical as each other? Differential geometry is a complete mess to try and unpack by yourself. The difference between k-forms and differential k-forms, what TpM and T*pM actually are and why their bases are the way they are, etc. etc.

@cubism_2 Ай бұрын

The highest level of geometry is the the kind that you can dash through

@CheckmateSurvivor Ай бұрын

No. It's finding the real shape of the Earth.

@themugwump33 20 күн бұрын

3:49 how does this change when you increase the number of dimensions? Is there an equation like “S sub n = blah blah blah” where S is the number of shapes and n is the number of dimensions?” S sub 3 = 5, what does S sub 4 equal? S sub 5? S sub n? Can you do the same with number of faces in the shape?

@كمالرامي-ع9س Ай бұрын

you forgot vectors

@nzubechukwu Ай бұрын

Nice video! Can you provide resources in future videos? Thanks!

@kevon217 Ай бұрын

Love your vids. Chopin in back is a nice relaxing touch!

@chevasit Ай бұрын

Good 👍

@KingLarbear Ай бұрын

I love these

@marcelob.5300 Ай бұрын

Dramatically outstanding. Thanks!

@randomchannel-px6ho Ай бұрын

Final boss: String Theory

@tomkerruish2982 Ай бұрын

6:17 wha??? x = r cos theta and theta = arctan y/x

@ThoughtThrill365 Ай бұрын

Good catch, looks like the cos and tan characters got duplicated on our software.

@johncunner2429 Ай бұрын

@@ThoughtThrill365 So as this answer, it appears :))

@Fepo.productions Ай бұрын

Maths is so funny and cool. It's basically its own language and I will label it as a language on my CV when I finish A-level maths.

@SparerRoom49700 Ай бұрын

2:45 This is not the full postulate

@Claudible Ай бұрын

but how do I turn a sphere outside in?

@CoopKeith1 Ай бұрын

At 0:49, the f do you mean secant? Your illustration is incorrect.

@memeing_donkey Ай бұрын

Google says a secant is a line that intersects a curve at a minimum of two distinct points. The word secant comes from the Latin word secare, meaning to cut. So yes the lines should intersect at two points, not one.

@HarmonicEpsilonDelta Ай бұрын

This is weird because in spanish two lines are called "secantes" if they intersect at one point. I am not sure it the wording may depend on the author or if there is no complete concensus on the word "secant"

@Slickz-Gtag Ай бұрын

Isn’t intersecting lines?

@BehrouzTotonchi Ай бұрын

All your vidoes are so amazing and very much appreciated sir.... PLEASE keep up the great work. As an engineer i learn a lot from your vast knowledge. Tnx❤

@dustangel7668 Ай бұрын

Why do you make Pythagorean theorem a separate entity at the very end of the first section? It is only a special case of cosine theorem. Sure, everybody knows the name (unlike that of cosine theorem) but it still doesn't change the fact that Pythagorean theorem is just a cosine theorem for right angle triangle.