## abacus

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## Abacus

# Abacus

The abacus is the most ancient calculating device known. It has endured over time and is still in use in some countries. An abacus consists of a wooden frame, rods, and beads. Each rod represents a different place value—ones, tens, hundreds, thousands, and so on. Each bead represents a number, usually 1 or 5, and can be moved along the rods. Addition and subtraction can easily be performed by moving beads along the wires of the abacus.

The word *abacus* is Latin. It is taken from the Greek word *abax*, which means "flat surface." The predecessors to the abacus—counting boards— were just that: flat surfaces. Often they were simply boards or tables on which pebbles or stones could be moved to show addition or subtraction. The earliest counting tables or boards may simply have been lines drawn in the sand. These evolved into actual tables with grooves in them to move the counters.

Since counting boards were often made from materials that deteriorated over time, few of them have been found. The oldest counting board that has been found is called the Salamis Tablet. It was found on the island of Salamis, a Greek island, in 1899. It was used by the Babylonians around 300 b.c.e. Drawings of people using counting boards have been found dating back to the same time period.

There is evidence that people were using abacuses in ancient Rome (753 b.c.e.–476 c.e.). A few hand abacuses from this time have been found. They are very small, fitting in the palm of your hand. They have slots with beads in them that can be moved back and forth in the slots similar to counters on a counting board. Since such a small number of these have been found, they probably were not widely used. However, they resemble the Chinese and Japanese abacuses, suggesting that the use of the abacus spread from Greece and Rome to China, and then to Japan and Russia.

## The Suanpan

In China, the abacus is called a "suanpan." Little is known about its early use, but rules on how to use it appeared in the thirteenth century. The suanpan consists of two decks, an upper and a lower, separated by a divider. The upper deck has two beads in each column, and the lower deck has five beads in each column. Each of the two beads in the ones column in the top deck is worth 5, and each bead in the lower deck is worth 1. The column farthest to the right is the ones column. The next column to the left is the tens column, and so on. The abacus can then be read across just as if you were reading a number. Each column can be thought of in terms of **place value** and the total of the beads in each column as the **digit** for that place value.

The beads are moved toward the middle beam to show different numbers. For example, if three beads from the lower deck in the ones column have been moved toward the middle, the abacus shows the number 3. If one bead from the upper deck and three beads from the lower deck in the ones column have been moved to the middle, this equals 8, since the bead from the upper deck is worth 5.

To add numbers on the abacus, beads are moved toward the middle. To subtract numbers, beads are moved back to the edges of the frame. Look at the following simple calculation (12 + 7 = 19) using a suanpan.

The abacus on the left shows the number 12. There is one bead in the lower deck in the tens place, so the digit in the tens column is 1. There are two beads in the lower deck in the ones place, so the digit in the ones column is 2. This number is then read as 12. To add 7 to the abacus, simply move one bead in the ones column of the top deck (5) and two more beads in the ones column of the lower deck (2). Now the suanpan shows 9 in the ones column and 10 in the tens column equaling 19.

## The Soroban

The Japanese abacus is called the soroban. Although not used widely until the seventeenth century, the soroban is still used today. Japanese students first learn the abacus in their teens, and sometimes attend special abacus schools. Contests have even taken place between users of the soroban and the modern calculator. Most often, the soroban wins. A skilled person is usually able to calculate faster with a soroban than someone with a calculator.

The soroban differs only slightly from the Chinese abacus. Instead of two rows of beads in the upper deck, there is only one row. In the lower deck, instead of five rows of beads, there are only four. The beads equal the same amount as in the Chinese abacus, but with one less bead, there is no carrying of numbers. For example, on the suanpan, the number 10 can be shown by moving the two beads in the upper deck of the ones column or only one bead in the upper deck of the tens column. On the soroban, 10 can only be shown in the tens column. The beads in the ones column only add up to 9 (one bead worth 5 and four beads each worth 1).

## The Schoty

The Russian abacus is called a schoty. It came into use in the 1600s. Little is known about how it came to be. The schoty is different from other abacuses in that it is not divided into decks. Also, the beads on a schoty move on horizontal rather than vertical wires. Each wire has ten beads and each bead is worth 1 in the ones column, 10 in the tens column, and so on. The schoty also has a wire for quarters of a ruble, the Russian currency. The two middle beads in each row are dark colored. The schoty shows 0 when all of the beads are moved to the right. Beads are moved from left to right to show numbers. The schoty is still used in modern Russia.

see also Calculators; Mathematical Devices, Early.

*Kelly J. Martinson*

## Bibliography

Pullan, J.M. *The History of the Abacus.* New York: Frederick A. Praeger, Inc., 1969.

## THE ABACUS VERSUS THE CALCULATOR

In late 1946 a Japanese postal official highly skilled in using the soroban (Japanese abacus) engaged in a contest with an American soldier in adding, subtracting, and multiplying numbers. The American used what was then the most modern electromechanical calculator. In four of five contests, the Japanese official with the soroban was faster, being beaten only in the multiplication problems.

## Abacus

# Abacus

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.

## Abacus

# Abacus

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.

## Abacus

# Abacus

The abacus is an ancient calculating machine. This simple apparatus is thought to have originated in Babylon about 5,000 years ago. Today, the abacus is still used commonly in Japan, China, the Middle East, and Russia. In China, the abacus is called a *suan pan,* meaning "counting tray." In Japan, it is called a *soroban.* Japanese school children are still taught how to use the *soroban,* and competitions are held annually to find the most skillful calculators.

Historians think that the first abacus consisted of a shallow tray filled with fine sand or dust. Numbers were recorded and erased easily with a finger. The word abacus, in fact, may have come from the Semitic word for "dust," *abq.*

A modern abacus is made of wood or plastic. It consists of a rectangular frame about the size of a shoe-box lid. Within the frame are at least nine vertical rods strung with moveable beads. A horizontal crossbar perpendicular to the rods separates the abacus into two unequal parts. The beads above the crossbar are known as heaven beads, and those below the crossbar are called earth beads.

The numerical value of each bead depends on its location in the abacus. Each heaven bead has a value of five times that of an earth bead below it. Each rod represents columns of written numbers. Beads on the vertical rod farthest to the right have their values multiplied by one. On this rod, each earth bead is one and each heaven bead is five. Beads on the second rod from the right, however, have their value multiplied by 10. On this rod, each earth bead represents 10 and each heaven bead stands for 50. Beads on the third rod from the right have their value multiplied by 100, so that each earth bead represents 100 and each heaven bead stands for 500, and so on.

To operate, an abacus is placed flat and all beads are pushed towards the outer edges, away from the crossbar. Beads are then slid upward or downward to represent a number. The number 7, for example, is represented by moving one heaven bead (worth 5) downward toward the crossbar and two earth beads (worth one each) upward toward the crossbar. The number 24 is represented by moving two earth beads on the second rod (worth 10 each) and four earth beads on the first rod (worth 1 each) upward. Addition, subtraction, and even lengthy multiplication and division problems can be solved with an abacus. Advanced users can even find the square root of any number.

[*See also* **Arithmetic; Mathematics** ]

## Abacus

# Abacus

The abacus, an ancient calculating device, probably originated in Babylon around 2400 B. C. E. as a "counting box." It was the world's first calculator, and contemporary versions are still in use today.

An abacus is a wooden or metal rectangular frame with vertical bars containing movable beads. Prior to the advent of the abacus, stones were used as computational tools. This had two major disadvantages: it was easy to lose track while figuring, and finding or transporting large numbers of stones was difficult. By contrast, the abacus was a highly portable, easy-to-use device that proved to be an excellent alternative to a bag of stones.

The abacus was used throughout the Middle East and as far eastward as Japan. The number of vertical bars and beads on each bar varied from culture to culture, but the basic function of the abacus—calculating the costs and quantities of goods—remained the same.

The Chinese abacus, which is the most familiar form today, divides the frame with a horizontal bar. The classic version, known as *suan-pan,* or the "2/5 abacus," is thought to have developed around C. E. 1200. The area above
the horizontal bar, heaven, contains two beads per vertical rod; each has a value of five. In the lower area, or earth, each vertical rod contains five beads, each with a value of one. Each vertical rod represents a unit of ten. Calculating is accomplished by moving beads toward or away from the horizontal divider. In the mid-1800s, the 2/5 abacus was replaced by the 1/5 abacus, and, by the 1930s, the most widely used form of abacus was the Japanese-made *soroban,* or 1/4 abacus.

Although pocket calculators and other devices have replaced the abacus in most parts of the world, many Asian shopkeepers and schoolchildren still use the abacus for basic arithmetic functions such as adding, subtracting, and multiplying.

**see also** Napier's Bones; Slide Rule.

*Bertha Kugelman* *Morimoto*

### Bibliography

Menninger, Karl. *Number Words and Number Symbols.* Cambridge, MA: M.I.T. Press, 1969.

#### Internet Resources

Ryerson University, Department of Electrical and Computer Engineering, *The Abacus: The Art of Calculating with Beads*. <http://www.ee.ryerson.ca:8080/~elf/abacus/>.

## abacus (in mathematics)

abacus (ăb´əkəs, əbăk´–), in mathematics, simple device for performing arithmetic calculations. The type of abacus now best known is represented by a frame with sliding counters. An elementary abacus might have ten parallel wires strung between two boards on a frame, with nine beads on each wire. Each bead on a given wire has the same value: either ten or some multiple or submultiple of ten. For example, all of the beads on a particular wire may have a value of 1, making this the units wire, or 10, making this wire the tens wire. Numbers are represented and added together on the abacus by grouping beads together. To represent 155, five beads on the units wire are separated from the others on that wire, five beads on the tens wire, and one bead on the hundreds wire. To add 243 to 155, three more beads on the units wire are slid over to join the group of five, four more beads on the tens wire join the five there, and two more beads on the hundreds wire join the one there. The number 398 is now represented on the abacus. Subtraction can be performed by separating groups of beads. More elaborate processes are used to perform multiplication and division. The abacus is used for calculating in the Middle East, Asia, and Russia and for teaching children the elements of arithmetic in many countries. An apparatus of pebbles or other movable counters was known in antiquity to the Egyptians, Greeks, Romans, and Chinese. A special merit of the abacus was that it simplified the addition and subtraction of numbers written in Roman numerals. Another type of abacus includes a board covered with sand or wax to facilitate making and erasing marks.

See J. M. Pullan, *The History of the Abacus* (1968); P. H. Moon, *The Abacus* (1971).

## abacus

**abacus (pl. abaci).** **1.** Flat-topped plate, also called *tailloir*, the upper member of a capital of a column on which the architrave rests. The Greek Doric abacus is the simplest, consisting of a square unmoulded block, called *plinthus*, but abaci vary according to the Order used.

**2.** Flat slab supported on a podium or legs, used as a sideboard or for the display of plate, etc., in Antiquity.

**3.** Panel on an Antique wall.

## abacus

**abacus**
•**Bacchus**, Caracas, Gracchus
•Damascus
•**Aristarchus**, carcass, Hipparchus, Marcus
•**discus**, hibiscus, meniscus, viscous
•umbilicus • Copernicus
•Ecclesiasticus • Leviticus • floccus
•**caucus**, Dorcas, glaucous, raucous
•**Archilochus**, Cocos, crocus, focus, hocus, hocus-pocus, locus
•autofocus
•**fucus**, Lucas, mucous, mucus, Ophiuchus, soukous
•ruckus • fuscous • abacus
•diplodocus • Telemachus
•Callimachus • Caratacus • Spartacus
•circus

## abacus

ab·a·cus / ˈabəkəs/ • n. (pl. -cus·es ) 1. an oblong frame with rows of wires or grooves along which beads are slid, used for calculating. 2. Archit. the flat slab on top of a capital, supporting the architrave.

## abacus

**abacus** an oblong frame with rows of wires or grooves along which beads are slid, used for calculating; possibly a development of the classical counting board, it was widely used in Europe in the Middle Ages and is still used in some countries.

The word in this sense dates from the late 17th century; it is recorded in late Middle English, denoting a board strewn with sand on which to draw figures, and comes via Latin from Greek *abax*, *abak-* ‘slab, drawing board’, of Semitic origin, and probably related to Hebrew *'āḇāq* ‘dust’.