Mathematicians from New York University and the University of British Columbia have resolved a decades-old geometric problem, the Kakeya conjecture in 3D, which studies the shape left behind by a needle moving in multiple directions.

The research is published on the arXiv preprint server.

The Kakeya conjecture was inspired by a problem asked in 1917 by Japanese mathematician Sōichi Kakeya: What is the region of smallest possible area in which it is possible to rotate a needle 180 degrees in the plane? Such regions are called Kakeya needle sets.