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 ...

But now, two mathematician friends have used their quarantine time to crack a variation of the age-old geometry problem. They analyzed a set of loopy shapes called smooth, continuous curves to prove ...

A geometry problem that has been puzzling scientists for 60 years has likely just been solved by an amateur mathematician with a newly discovered 13-sided shape. Called “The hat” because it vaguely ...

Debates over how geometry is understood and learned date back at least to the days of Plato, with more recent scholars concluding that only humans ...