The world of geometry just witnessed a pivotal breakthrough. Mathematicians at Monash University have cracked a centuries-old puzzle dating back to the 17th century, extending Descartes’ Circle ...

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 ...

Computers are working to solve an age-old geometry problem. Humans can’t “square the circle” by hand, which was proven in the 1800s. Computer solutions involve infinity, complexity, and some ...

Here’s a simple-sounding problem: Imagine a circular fence that encloses one acre of grass. If you tie a goat to the inside of the fence, how long a rope do you need to allow the animal access to ...

A red circle is inscribed inside a blue square. The arrangement leaves gaps in the square’s four corners, two of which are filled with smaller circles that just barely touch the big red circle and the ...