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FIRST I GOT GOOSEBUMPS but then i saw its nothing new and its totally boring

amazing❤

This video was great ! As a lover of trig functions its rare to see videos like these , it would be better if you recommended sources for more exploration of the topic .

This is a really good video.

Absolutely brilliant. U made this complex topic look so easy. Can't wait video about " applications of elliptic functions in nonlinear mechanics" in ur representation .It would be great if u ll made such video. Without elliptic functions it isn't possible to solve rigid body dynamic equations or non small angle pendulum equations of motion. Again thank u so much for ur great video

What program do you use for writing? How did you make the background? the video is great

So, I would say my vote does not matter most of the time since they call the election before even opening my letter, and the voting block that I'm a part of is too diluted between the fifty states. (This is my initial argument before viewing.)

Yes

The radical left are really irrational

Interesting video ruined by the idiotic background music

How can the universe expand faster than the speed of light? Does it had negativ mass? Maybe there is some unknown explaination for its behavior, physics applied in other parts of the universe might be diffrent. A blackhole might be similair to the expansion.

Thank you for the delicious understanding of a coffee.😊😊

Your statement about the eigenvalues being max and min values at 3:50 is only true for 2d vector space (so that there are only two eigenvalues - the max and min). 👍

this is great i have never seen a greater introduction to modular forms as this 2 part series, you allow me to understand. is there any book or video that you recomend to understand it relations to q series and theta functions?

music is a bit intrusive. otherwise, excellent.

thanks man

I absolutely love this video: content, backdrop, music, etc all of it. Thank you!

C1 isnt equal to -1. Clearly theres a mistake

Fucking hell their using U.S. Customary units.

"pounds per gallon" sounds like something from a Victorian textbook. I suppose I should be relieved that you Americans don't have your own archaic unit of time.

they had it coming

How can you wrote n ->Infinity when n<z (and z is not a infinite number)

“Ant Hill high school” 😂

Euler bless you and Euler bless this channel

As an end for 2023, I’m happy I found this channel to start the next year with. Having been away from pure maths and not being much proficient in some of these core underlying terms, I can’t say i fully understood it but it makes me equally as happy. Fantastic video ❤

great channel!

Excellent video, explanations are easy to understand. Will definitely wait for part 2!

❤❤

It is a great video. But I felt like you rushed through this video. Could have been better if you followed a slower pace, even if the video would become quite large.

great

Somewhere out there is a 12-year-old who, after seeing this video, will realize that he wants to be a mathematician.

Phrases like 'calculus 2' mean nothing to anyone outside of your one country.

Please discuss elliptic curve and modular form

Pls look into geometric algebra

This just seems wrong. Imagine if all the internal space of the toroid was filled with really long strings. Would only the strings along the edge wrap around to their end points of would strings in the middle also wrap around to their endpoints. Basically it seems like it should be a sphere or infinite space or a physical barrier along the edge because at the center of the ring on the toroid-let me rephrase this point. If you took a donut with a hole in the middle of it and put in on the table and took a knife and cut it perfectly in half you would see that you now have two circles where the ring crossed through to the other half of the donut. Now in the very center of one of those two circles would space wrap around to itself in a tighter and tigger circle to closer you got to the center of one of the two circles (in the toroidal model of spacetime)? Probably not. What I'm suggesting is that there would be a sorties paradox there to be seen if conceptualize correctly that on one hand you have the edge of the circle which wraps around to itself right? And on the other hand, in the center of the circle you either have just space without any wrapping around onto itself, or a tighter and tighter string that wraps around to its own end getting smaller and smaller the closer you get to the center of the ring of the toroid. It's really hard to explain without being able to point physically at what I'm talking about but it makes more sense that there is a physical wall somewhere out there in the universe or there is just endless space without bounds. Just a thought

Thank you. This is very helpful.

your channel is underrated....thank you for your work!

These inventions were already done by several hindu mathematicians way before than european christian mathematicians

Awesome

good job, but make music louder next time

So, where do you lie (or, perhaps better-worded, what is your position) on the pi v. tau debate?

Just as a curve can be defined (whether geometrically, trigonometrically, via calculus, or any other higher math) in terms of a line, a line can in turn be defined in terms of a curve, describing it as the perimeter (or segment of that perimeter) of a circle whose radius is of infinite length

It's all pretty obvious if you think about it.

When you think of time. It is a constant angle contours. So time is seen as the shortest path possible between different points. Even structures take the shape of an egg are more stable. A shape of the sphere is just closer to time though not exact. Even the sun is somewhat like egg shaped though far it looks spherical. They are egg shaped because it has to push through space for linearity of time. No two things have the same frequency. Resonance is always orthogonal.

Thank you. Well done.

But what are principal directions? If for example we rotate a hyperbolic paraboloid z=x^2-y^2 along OZ will they change? Or are they just sections of a surface by a surfaces of constant u or v?

Americans love shoving their thanksgiving thing down everyone else's throats, don't they.

Hi

Time creates curved surfaces. Though they are same anywhere. Powers create time singularity.