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 ...

Arc length is a fraction of circumference. Area of a sector is a fractions of the area of a circle. Both can be calculated using the angle at the centre and the diameter or radius. Practice circle ...

Three mathematicians show, for the first time, how to form a square with the same area as a circle by cutting them into interchangeable pieces that can be visualized. Around 450 BCE, Anaxagoras of ...

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 ...