# Abacus

### beads earth heaven rod

The abacus is an ancient calculating machine. This simple apparatus is about 5,000 years old and is thought to have originated in Babylon. As the concepts of **zero** and Arabic number notation became widespread, basic math functions became simpler, and the use of the abacus diminished. Most of the world employs adding machines, calculators, and computers for mathematical calculations, but today Japan, China, the Middle East, and Russia still use the abacus, and school children in these countries are often taught to use the abacus. In China, the abacus is called a suan pan, meaning counting tray. In Japan the abacus is called a soroban. The Japanese have yearly examinations and competitions in computations on the soroban.

Before the invention of counting machines, people used their fingers and toes, made marks in mud or sand, put notches in bones and wood, or used stones to count, calculate, and keep track of quantities. The first abaci

were shallow trays filled with a layer of fine sand or dust. Number symbols were marked and erased easily with a finger. Some scientists think that the term *abacus* comes from the Semitic word for dust, *abq*.

A modern abacus is made of wood or plastic. It is rectangular, often about the size of a shoe-box lid. Within the rectangle, there are at least nine vertical rods strung with movable beads. The abacus is based on the decimal system. Each rod represents columns of written numbers. For example, starting from the right and moving left, the first rod represents ones, the second rod represents tens, the third rod represents hundreds, and so forth. A horizontal crossbar is **perpendicular** to the rods, separating the abacus into two unequal parts. The moveable beads are located either above or below the crossbar. Beads above the crossbar are called heaven
beads, and beads below are called earth beads. Each heaven bead has a value of five units and each earth bead has a value of one unit. A Chinese suan pan has two heaven and five earth beads, and the Japanese soroban has one heaven and four earth beads. These two abaci are slightly different from one another, but they are manipulated and used in the same manner. The Russian version of the abacus has many horizontal rods with moveable, undivided beads, nine to a column.

To operate, the soroban or suan pan is placed flat, and all the beads are pushed to the outer edges, away from the crossbar. Usually the heaven beads are moved with the forefinger and the earth beads are moved with the thumb. For the number one, one earth bead would be pushed up to the crossbar. Number two would require two earth beads. For number five, only one heaven bead would to be pushed to the crossbar. The number six would require one heaven (five units) plus one earth (one unit) bead. The number 24 would use four earth beads on the first rod and two earth beads on the second rod. The number 26 then, would use one heaven and one earth bead on the first rod, and two earth beads on the second rod. **Addition**, **subtraction**, **multiplication**, and **division** can be performed on an abacus. Advanced abacus users can do lengthy multiplication and division problems, and even find the **square root** or cube root of any number.

See also Arithmetic; Mathematics.

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