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 ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

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 ...

THIS work of Prof. Smith's has a “very practical purpose,” viz, “to present in simple and intelligible form a body of geometric doctrine, acquaintance with which may fairly be demanded of candidates ...