Unsolved Problem 13:
Is there a point in the plane that is at a rational
distance from each of the four corners of a unit square?
A rational number is a number that is the
ratio of two integers.
A unit square is a square of side length 1.
Rational Distances to the Vertices of a Square
- [Boroczky 1987]
- K. Böröczky and G. Fejes Tóth,
North-Holland Publishing Company. New York: 1987.
Each week, for your edification, we publish a well-known
unsolved mathematics problem. These postings are intended
to inform you of some of the difficult, yet
interesting, problems that mathematicians
are investigating. We do not suggest that you tackle these problems,
since mathematicians have been unsuccessfully working on these
problems for many years.