Mathematician Jordan Ellenberg answers the internet's burning questions about geometry. How are new shapes still being discovered? Where are we using Pythagorean theorem in real life? How many holes ...

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 ...

Forbes contributors publish independent expert analyses and insights. Ray Ravaglia covers education, focusing on technology and innovation. On any given day, 600+ million students worldwide will work ...