Genaille–Lucas rulers (also known as Genaille's rods) are an arithmetic tool invented by Henri Genaille, a French railway engineer, in 1891. The device is a variant of

Napier's bones Napier's bones is a manually-operated calculating device created by John Napier of Merchiston, Scotland for the calculation of products and quotients of numbers. The method was based on lattice multiplication, and also called ''rabdology'', a wor ...

. By representing the

carry Carry or carrying may refer to: People *Carry (name) Finance * Carried interest (or carry), the share of profits in an investment fund paid to the fund manager * Carry (investment), a financial term: the carry of an asset is the gain or cost of h ...

graphically, the user can read off the results of simple multiplication problems directly, with no intermediate

mental calculation Mental calculation consists of arithmetical calculations using only the human brain, with no help from any supplies (such as pencil and paper) or devices such as a calculator. People may use mental calculation when computing tools are not availab ...

History

In 1885, French mathematician

Édouard Lucas __NOTOC__ François Édouard Anatole Lucas (; 4 April 1842 – 3 October 1891) was a French mathematician. Lucas is known for his study of the Fibonacci sequence. The related Lucas sequences and Lucas numbers are named after him. Biography 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. He presented his invention to the Académie française in 1891. The popularity of Genaille's rods was widespread but short-lived, as

mechanical calculator A mechanical calculator, or calculating machine, is a mechanical device used to perform the basic operations of arithmetic automatically, or (historically) a simulation such as an analog computer or a slide rule. Most mechanical calculators we ...

s soon began to displace manual arithmetic methods.

Appearance

A full set of Genaille–Lucas rulers consists of eleven strips of wood or metal. On each strip is printed a column of triangles and a column of numbers: Genaille-Lucas rulers full

Multiplication

By arranging these rulers in the proper order, the user can solve multiplication problems. Consider multiplying 52749 by 4. Five rulers, one for each digit of 52749, are arranged side-by-side, next to the "index" ruler: The second multiplicand is 4, so we look at the fourth row: We start from the top number in the last column of the selected row: The grey triangle points the way to the next number: We follow the triangles from right to left, until we reach the first column. Then we simply read off the digits that we visited. The product, shown in red, is 210996.

Division

Soon after their development by Genaille, the rulers were adapted to a set of rods that can perform division. The division rods are aligned similarly to the multiplication rods, with the index rod on the left denoting the

divisor In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by ...

, and the following rods spelling out the digits of the dividend. After these, a special "remainder" rod is placed on the right. The

quotient In arithmetic, a quotient (from lat, quotiens 'how many times', pronounced ) is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a ...

is read from left to right, following the lines from one rod to the next. The path of digits ends with a number on the remainder rod, which is the

remainder In mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient ( integer division). In algeb ...

given by the division.

Resources

References

External links

History of computers and computing: Napier's bones
Describes the use of Genaille–Lucas rulers. {{DEFAULTSORT:Genaille-Lucas rulers Mechanical calculators Multiplication