Genaille–Lucas rulers

By representing the carry graphically, the user can read off the results of simple multiplication problems directly, with no intermediate mental calculations.

In 1885, French mathematician Édouard Lucas posed an arithmetic problem during a session of the Académie française.

Genaille, already known for having invented a number of arithmetic tools, created his rulers in the course of solving the problem.

The popularity of Genaille's rods was widespread but short-lived, as mechanical calculators soon began to displace manual arithmetic methods.

By arranging the rulers in the proper order, the user can find unit multiples of short natural numbers by sight.