The Hairy Ball Theorem—you can never comb a hairy sphere com...

Prompt

The Hairy Ball Theorem—you can never comb a hairy sphere completely flat: there will always be at least one point where the hair stands up or forms a cowlick (a zero vector). It was proved by Henri Poincaré in the 1880s and later by Brouwer in 1912, and it applies to any continuous tangent vector field on a sphere. This means that at any moment, there must be at least one point on Earth's surface where the horizontal wind speed is exactly zero, such as the eye of a cyclone. The strange part is that a torus (donut) can be combed perfectly flat, so the shape of the surface decides everything—I need you to make me a 45-second, highly detailed and professional 2D + 3D animated video, with a plain white background in 3:4 aspect ratio to explain this concept, for YouTube Shorts, with very fast and dynamic camera movement, in a single HTML file, also add a download button to download the video in 2K to 4K resolution.

A system prompt was added to support web rendering