How to Get to Gaussian Curvature Naturally
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- Опубликовано: 12 окт 2024
- PDF summary link
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Inspired by this book
amzn.to/3Ykj7ZX
And this paper
blogs.goucher....
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Thanks for the explanation.
You, such a great video, another level each time!)
@@SobTim-eu3xu thanks for the amazing comment of encouragement (as always!!!) 😎
I just wanted to say; keep doing what you're doing because I love your videos! I hope one day many people discover this channel. I shared one of your videos to a friend and it helped them a lot too. The animation is beautiful and I love how you explain difficult concepts with ease :D
@leventeabraham6906 Wow, thank you so much for your nice words, Levente. You have no idea how much it means to us! We will definitely keep going and increasing the quality even more of the videos, as well as the quantity of videos we publish per week. Please, let us know how we can help you, i.e. what kind of content would be useful to you 😎
@@dibeos I have all my respect for you two making these visual videos! In my free time I like to learn new math topics and this channel is the motivation. I think a video on Laplace transform would be interesting. I am an undergraduate mechatronics engineer and we use this all the time for system controls and solving differential equations. I think it would help others engineers too 😊
This is Differential Geometry on a beautiful Visualisation
@@Prof_Michael yes, we thought about putting “differential geometry” in the title, but “Gaussian curvature” seemed more appropriate. Anyway, this week we will publish another one going deeper on differential geometry
@@dibeos very good…
I’m also working on starting my channel and solving Mathematics related problems from Calculus I & II (because I Love Sir Isaac Newton so much, hopefully you’ll make a video devoted to Newton), Laplace Transform, Fourier Transform, Z Transform, Matrix Algebra, Probability Theories like Bivariate Normal distributions etc..
@@Prof_Michael woooow, i love these subjects as well, really. Please let me know when you post videos about them, I want to watch
I'm wondering how do intrinsic curvatures add up in 3-D?
Let's say we have a transformation or process (F1) that generates curvature k1 at point P in 3-D. Another process F2 would generate k2 at the same point. Now, what is the curvature K at P if we apply both transformation in succession?
What is curvature at P after F1(F2(P))?
Do they commute?
F1(F2(P)) = F2(F1(P)) ?
Is K = k1 + k2 ?
I wonder:is the circle the only object with constant curvature at every single point?
There's the reverse circle which has negative curvature at every point. It looks like a cone.
@@daniel_77.
I remember watching some video of Andrew university where the question was answered. It was one of many in a playlist about the local theory of space curves (or something like that? I don't remember exactly)
I'll reply again with more details.
@@adiaphoros6842 Don't you mean the inverse sphere?
I believe there is a theorem which states that the curvature and torsion of a curve will determine a curve up to translation and direction. For a plane curve, the torsion is 0. So all curves with a fixed constant curvature are the same (up to translation and direction traversed), i.e., they are all circles with radius 1/k.
Channel name: Math at Andrew university.
Playlist: differential geometry
I couldn't find which video it was, sorry 😅 .
Your question is also related to a bigger question: can we uniquely determine the shape of a curve just from its curvature and torsion?
And the answer is yes! This is called the fundamental theorem of space curves.
Awesome!
The link to Garman & Bonnie's paper is broken. Please fix.
Fixed it, their link was broken but we found another one 👍🏻
@@dibeos Thanks, prima!
@tonibat59 prego ;)
COol
@@jammasound please, let us know what kind of content you’d like to see in the channel 😎
@@dibeos geometry, algebra, calculus, probability
@@jammasound straight to the point! 👌🏻thanks! 😎