Fascinants carrés magiques

Even in mathematics, kingdom of rigor, one cannot escape the necessity of making approximations or roundings, of bounding deviations or potential errors. The handling of floating-point numbers, which bridges the world of ideas and that of technology, is a fine example. The goal of exactitude pushes one to quantify the uncertainty imposed by technical or material constraints. Inseparable from scientific computing, including with computer tools, approximation can have far-reaching consequences. Yet some errors are famous for having, inadvertently, allowed a door to be opened toward a new universe.

For centuries, enthusiasts of elegant arithmetic have vied with each other in ingenuity to propose ever more astonishing magic squares, with increasingly numerous properties. One of the experts in the field, René Descombes, shares some of his construction methods. While computer tools allow enthusiasts to expand their collection of achievements, variants continue to increase. Let us rediscover multiplicative magic squares, pandigital magic squares and other "magic" constructions. The arithmetic treasures they contain seem limitless and are even found in figurative art.