The abstract Mathematical Concepts of the Cox-Zucker Machine and Hairy Ball Theorem have a fight. Fight takes place in the Platonic World of Forms.
R1) Speed Equalized
How do I prove that that a non-vanishing continuous tangent field exists for odd dimensional n spheres?
Also an intuitive proof for hairy ball theorem that doesn't use the Euler characteristic.
I was following this worksheet I found on the internet. http://www.math.toronto.edu/safibn/Teaching/HBT.pdf
The Euler Characteristic proof starts from page 5. I solved
15 : Euler characteristic is 2
17 : Assumed this
18 : Charge is 2 ?
But couldn't solve 16, 19 and 20. How do I go about it?
did u know it was prooved that sphere of vectors in an even dimension could not be directed all towards the same direction. In other terms, a hairy ball cannot be entierly capped, it will either have a spike or a hole, therefore baldness
She said it was 'inappropriate' and 'to complicated'. Anybody know some simple-ish math-related stuff I can use instead?
I was hoping someone could quickly explain to me why the hairy ball theorem implies that the tangent bundle of S^2 is non trivial
https://en.wikipedia.org/wiki/Hairy_ball_theorem
https://en.wikipedia.org/wiki/Lint_(material)#Navel_lint
"One hypothesis is that hair travels along a lint highway defined as integral curves of the vector field given by the direction of growth of the hair, which must end at a vanishing point according to the hairy ball theorem."
