New Proof Threads the Needle on a Sticky Geometry Problem

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…

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