The "hairy ball theorem". (a) Vector fields smoothly "combed" on a 2... | Download Scientific Diagram
![MathType on X: "The Hairy Ball theorem or Hedgehog theorem proven by Poincaré in the 19th century states that "you can't comb a hairy ball flat without creating a cowlick". A hairy MathType on X: "The Hairy Ball theorem or Hedgehog theorem proven by Poincaré in the 19th century states that "you can't comb a hairy ball flat without creating a cowlick". A hairy](https://pbs.twimg.com/media/EBdCHWCWwAU3QOj.jpg:large)
MathType on X: "The Hairy Ball theorem or Hedgehog theorem proven by Poincaré in the 19th century states that "you can't comb a hairy ball flat without creating a cowlick". A hairy
![Hairy ball theorem A failed attempt to comb a hairy 3-ball (2-sphere), leaving a tuft at each pole A hairy doughnut (2-torus), on the other hand, is quite easily combable. - iFunny Hairy ball theorem A failed attempt to comb a hairy 3-ball (2-sphere), leaving a tuft at each pole A hairy doughnut (2-torus), on the other hand, is quite easily combable. - iFunny](https://imageproxyb.ifunny.co/crop:x-20,resize:640x,quality:90x75/images/1e6ac87637fd07463a5105bc81a4ac8f6a5d136f867a159db7666fa15612d874_1.jpg)
Hairy ball theorem A failed attempt to comb a hairy 3-ball (2-sphere), leaving a tuft at each pole A hairy doughnut (2-torus), on the other hand, is quite easily combable. - iFunny
![differential geometry - Hairy Ball Theorem on $\mathbb{S}^2$: a counter-example? - Mathematics Stack Exchange differential geometry - Hairy Ball Theorem on $\mathbb{S}^2$: a counter-example? - Mathematics Stack Exchange](https://i.stack.imgur.com/3uGoF.png)