What are Manifolds?

Hey everyone! Welcome to Euler's Quanta. In this video, I try to give as much intuition as possible into the idea of a manifold, while introducing some of the rigorous yet beautiful ideas behind it (this video also serves as my entry to 3Blue1Brown's SoME1). Here are some references for those of you who want to know more about the topic:

- John M. Lee. Introduction to Smooth Manifolds. Springer Graduate Texts in Mathematics. 2013.
- Jon Pierre Fortney. A Visual Introduction to Differential Forms and Calculus on Manifolds. Birkhäuser. 2018.

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The animations and pictures appearing in this video are all my creation.

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Credits of the music:

1)
Track: Chopin - Fantaisie - Impromptu, Op. 66

2)
Winter Chimes by Kevin MacLeod
Creative Commons — Attribution 3.0 Unported— CC BY 3.0

[JariJaarvanen]

Just in case the builder of this masterpiece should ever come back to his creation, I want him to know that I have seldomly seen such a sophisticated while clear video regarding a math subject. Really looking forward to witness the next upload! Cheers!

[joeyphar]

legit peak content bro. the animations were a perfect companion to your already wonderful lecture. hope you do another vid one day!

[saransrimathi]

BRO THANK YOU, I was trying to warp my head around this for quite some days I watched many videos but they were either too technical as I am a beginner I couldn't understand it, but your video made a lot of sense on point crisp

[TheTacticalDood]

Cool! However, the music is a little bit loud so it is hard to focus. But good work nevertheless.

[kron]

Damn, Im about the thrid quarter and I am understanding everything perfectly, thank you, keep going :3

[Qsalis]

This is a very pretty video, and I hope you learn 2 channel audio soon :)