[ Frostigita ]

Je ĉi tago, mi ekvidis eksemplon de la erinaca aŭ harplenapilko teoremo postulis de Sr. Henri Poincaré.

Estas neeble kombi harojn sur pilko platen sen almenaŭ unu kalva punkto. Alivorte, ĉiam eksistas unu loko sur globo kie la vento ne blovas.

Li diras ke estas neniu nenula kontinua tangenta vektorakampo sur paraj-dimensiaj n-sferoj. #nerd

~pikiloe pilko~ Bv.K.

\eZ

#miksang #dailypic #aphotoaday
#Esperanto #photography #photo
#winter #snow #ice #frost #frozen
#Poincare #HenriPoincare
#hairyballtheorem #hedgehogtheorem
#algebraictopology
#spikes #spikey

Hairy ball theorem - Wikipedia

The hairy ball theorem from topology states that a hairy ball can't be combed flat without creating a cowlick or a bald spot, with surprising applications in meteorology, radio transmission, and nuclear power.

#HairyBallTheorem #Topology #MathFun

https://www.scientificamerican.com/article/maths-hairy-ball-theorem-has-surprising-implications/?utm_source=flipboard&utm_content=HariTulsidas%2Fmagazine%2FMind+and+Matter

Math’s ‘Hairy Ball Theorem’ Has Surprising Implications

Here’s what the hairiest problem in math can teach us about wind, antennas and nuclear fusion

Scientific American

Topology in real life!

"Perhaps the coolest application of the #HairyBallTheorem concerns nuclear fusion power."

"There’s a fundamental engineering hurdle when building fusion reactors: How do you contain plasma that’s 10 times hotter than the sun’s core? No material can withstand that temperature without disintegrating into plasma itself. So scientists have devised a clever solution: they exploit plasma’s magnetic properties to confine it within a strong magnetic field. The most natural container designs (think boxes or canisters) are all topologically equivalent to spheres. A magnetic field around any of these structures would form a continuous tangent vector field, and at this point we know what befalls such hairy constructions. A zero in the magnetic field means a leak in the container, which spells disaster for the whole reactor. This is why the leading design for fusion reactors, the tokamak, has a doughnut-shaped chamber. The International Thermonuclear Experimental Reactor (ITER) megaproject plans to finish construction of a new tokamak in France by 2025, and those involved claim their magnetic confinement system will be “the largest and most integrated superconducting magnet system ever built.”

"That’s #topology playing its part in our clean energy future."

https://www.scientificamerican.com/article/what-is-the-future-of-fusion-energy/

Image: This sphere is covered in small lines resembling hairs that are all combed in the same direction. Tufts on either side demonstrate the hairy ball theorem. Credit: Buckyball Design

What Is the Future of Fusion Energy?

Nuclear fusion won’t arrive in time to fix climate change, but it could be essential for our future energy needs

Scientific American
- As vector fields, they are not globally orthonormal; they are neither orthogonal, nor of unit length for points in general position. They cannot be globally normalized #hairyballtheorem in that one "cannot comb the hair on a sphere without leaving a tuft or a bald spot".