## Rectangles in a circle

Due to the exit restrictions imposed by the corona virus, two mathematicians were able to devote themselves to a decades-old geometric puzzle. At first they had little hope - but thanks to a trick, the solution was suddenly in front of them.

As the new coronavirus spread around the world in March 2020 and most states gradually imposed lockdowns, mathematicians Joshua Greene from the University of Durham in England and Andrew Lobb from the Okinawa Institute of Science and Technology found each other in Japan isolating again in their respective homes. In order to cope with the unfamiliar situation, the two colleagues decided to throw themselves into their research.

One of the problems the two friends tackled is a decades-old geometry question: Can you always mark four points in a closed curve (a loop that ends where it started) so that a rectangle with all conceivable aspect ratios is created? "The problem is simple to state and easy to understand, but it's really complicated," says knot theorist Elizabeth Denne of Washington and Lee University.

At first glance, it looks like a math competition problem that a junior high school student could solve with a ruler and compass. In reality, however, it has defied the best efforts of mathematicians for decades. When Greene and Lobb tackled it, they had no particular reason to expect to do betterâ€¦