kvadraterproblem

The "kvadraterproblem," also known as the squaring the square problem, is a mathematical puzzle that seeks to tile a perfect square with smaller, distinct perfect squares. The challenge lies in finding a solution where all the smaller squares have different side lengths. This problem is a specific case of the more general problem of tiling a rectangle with distinct squares.

The problem was first posed in the early 20th century. Early attempts focused on finding solutions for rectangles, and it was not until 1939 that the first perfect squared rectangle was discovered. The squaring the square problem, however, proved to be significantly more difficult. It was not until 1940 that the first perfect squared square was found by Roland Sprague.

The smallest perfect squared square found to date contains 21 distinct smaller squares. Solutions to this problem are often represented as diagrams or electrical network analogies. The complexity arises from the geometric constraints and the requirement for all squares to be of different sizes. Finding new solutions, especially with fewer squares, remains an area of interest for recreational mathematicians. The problem has connections to graph theory and electrical circuit theory, particularly through the concept of electrical networks.