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Kakeya needles: tubes in every direction (3D)
About this app
How tightly can needles pointing in many different directions be pushed together? The Kahane construction as a bundle of 16, 256 or 4096 tubes: pushed together, the volume of the union shrinks, but only logarithmically slowly, more slowly than any power of the thickness δ. Glowing needle through all directions, chart 2D versus 3D, planar Besicovitch set. Result from openai/math (family 074): Kakeya maximal conjecture in 3D, full dimension in 4D. Exhibit-ready.
Subject: Open problems, solved by AI
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