A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures. The post New Proof Threads the Needle on a Sticky Geometry Problem first appeared on Quanta Magazine
In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an infinitely thin, inch-long needle on a flat surface, then rotate it so that it points in every direction in turn. What’s the smallest area the needle can sweep out? If you simply spin it around its center, you’ll get a circle. But it’s possible to move the needle…