The original version of this story appeared in 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 ...

In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...

Gear-obsessed editors choose every product we review. We may earn commission if you buy from a link. Why Trust Us? A mathematician may have just proved the impossible possible. For 30 years, ...

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 ...