The Circle on the Chessboard


A chessboard has squares that are two inches on the side. What is the radius of the largest circle that can be drawn on the board in suche way that the circle’s circumference is entirely on black squares?

The Answer:
If you place the point of a compass at the centre of a black square on a chessboard with two-inch squares, and extend the arms of the compass a distance equal to the square root of 10 inches, the pencil will trace the largest possible circle that touches only black squares.