@@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.
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.
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.
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"
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?
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.
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❤
This video is like a Chat GPT answer.
You pretty much summed up the channel's content.
the voice sounds like AI too
The amount of misinformation confounded me
Please elaborate and provide additional details.
@@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.
@@iteo7349 thanks for this forewarning :)
I wanna know what you mean by this as someone who doesn't understand the video
The equation at 5:00 is also wrong 😂. It should be just y-y1=m(x-x1)
There are multiple errors and misconstruals in this video, unlike the others in this series.
Yeah I thought that point-slope formula was y-y1=m(x-x1) not with the +b
@@solar_aintdead4270 I think that it was meant to be like slope intercept when calculating an equation. I could be wrong though.
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.
... at least as far as I'm concerned. Don't cite me as a source or sth.
you forgot vectors
The highest level of geometry is the the kind that you can dash through
No. It's finding the real shape of the Earth.
Nice video! Can you provide resources in future videos? Thanks!
Love your vids. Chopin in back is a nice relaxing touch!
Amazing video mate
Dramatically outstanding. Thanks!
Final boss: String Theory
but how do I turn a sphere outside in?
6:17 wha??? x = r cos theta and theta = arctan y/x
Good catch, looks like the cos and tan characters got duplicated on our software.
@@ThoughtThrill365 So as this answer, it appears :))
At 0:49, the f do you mean secant? Your illustration is incorrect.
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.
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"
Isn’t intersecting lines?
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?
Good 👍
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.
I love these
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.
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❤
Which geometry uses Quantum Mechanics ?
Where do fractals come in here?
theyre kinda their own thing and appear randomly with not that much use to them, but id say somewhere around 4 and 5 is where you see them a bunch
2:45 This is not the full postulate
All my homies love some algebraic geometry 🤙 manifold action
UA-cam is automatically dubbing your recent permissions without your permission
It’s enabled by default
what about Numerical Geometry, the next level
👍
This channel deserves a million subscribers. Come on!