Math's 'hairy ball theorem' shows why there's always at least one place on Earth where no wind blows

Abstraction: Hairy ball theorem and its real-world consequences in physics and engineering

Key points:

• Hairy ball theorem (topology): no continuous nonvanishing tangent vector field can exist on a sphere — there must always be a zero (bald spot/cowlick) or discontinuity
• Applies to any shape topologically equivalent to a sphere (cubes, cylinders); does not apply to tori (doughnuts), which can be combed smoothly
• Wind on Earth's surface is a continuous tangent vector field on a sphere, so there must always be at least one point where wind speed is zero
• Isotropic antennas (broadcasting equal signal strength in all directions) are physically impossible because radio wave electric fields form a tangent vector field on the sphere of wavefronts
• Tokamak fusion reactors use a doughnut (torus) shape precisely to avoid the magnetic field zeros mandated for spherical containment — a zero in the field means a plasma leak

Connections: Topology · Vector Fields · Mathematical Physics

Source: https://www.livescience.com/physics-mathematics/mathematics/maths-hairy-ball-theorem-shows-why-theres-always-at-least-one-place-on-earth-where-no-wind-blows