# Abacus

Template:About
An **abacus** is a calculation tool, often constructed as a wooden frame with beads sliding on wires. It was in use centuries before the adoption of the written Arabic numerals system and is still widely used by merchants and clerks in China and elsewhere.

Although often attributed to the Chinese, the abacus is thought to have been invented by the Babylonians around 2400 BC. The first abacus was almost certainly based on a flat stone covered with sand or dust. Lines were drawn in the sand and pebbles used to aid calculations. From this, a variety of abaci were developed; the most popular were based on the bi-quinary system, using a combination of two bases (base-2 and base-5) to represent decimal numbers

The use of the word *abacus* dates back to before 1387 when a Middle English work borrowed the word from Latin to describe a sandboard abacus. The Latin word came from *abakos*, the Greek genitive form of *abax* ("calculating-table"). Because *abax* also had the sense of "table sprinkled with sand or dust, used for drawing geometric figures," it is speculated by some linguists that the Greek word may be derived from a Semitic root, *ābāq*, the Hebrew word for "dust." Though details of the transmission are obscure, it may also be derived from the Phoenician word *abak*, meaning "sand".

## Contents

## Roman abacus

*Main article: Roman abacus*

The Late Empire Roman abacus shown here in reconstruction contains seven long and seven shorter grooves, the former having up to five beads in each and the latter one.

The groove marked I indicates units, X tens, and so on up to millions. The beads in the shorter grooves denote fives—five units, five tens, *etc.*, essentially in a bi-quinary coded decimal system, obviously related to the Roman numerals. The short grooves on the right may have been used for marking Roman ounces.

Computations are made by means of beads which would probably have been slid up and down the grooves to indicate the value of each column.

## Chinese abacus

*Main article: Chinese abacus*

The **suanpan** (Template:Zh-stp) of the Chinese is similar to the Roman abacus in principle, though has a different construction.

The Chinese abacus is typically around 20 cm (8 inches) tall and it comes in various widths depending on the application. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads each in the bottom for both decimal and hexadecimal computation. The beads are usually rounded and made of a hard wood. The beads are counted by moving them up or down towards the beam. The abacus can be reset to the starting position instantly by a quick jerk along the horizontal axis to spin all the beads away from the horizontal beam at the center.

Chinese abaci can be used for functions other than counting. Unlike the simple counting board used in elementary schools, very efficient suanpan techniques have been developed to do multiplication, division, addition, subtraction, square root and cube root operations at high speed.

**Bead arithmetic** is the calculating technique used with various types of abaci, in particular the Chinese abacus.

## Japanese abacus

The Japanese eliminated (first) one bead from the upper deck and (later) another bead from the lower deck in each column of the Chinese abacus. The Japanese also eliminated the use of Quichu (Chinese division table). The method of Chinese division table was still used when there were 5 lower beads. There came the war of the Multiplication Table versus the Division Table. The school of Multiplication table prevailed in 1920s. The rods (number of digits) increase to usually 21, 23, 27 or even 31, thus allowing calculation for more digits.

Soroban is taught in elementary schools as a part of lessons in mathematics. When teaching the soroban, a song-like instruction is given by the tutor. The soroban is about 8 cm (3 inches) tall. The beads on a soroban are usually shaped as a double cone (bi-cone) to facilitate ease of movement.

Ironically, the primary students bring along with them two soroban, one with 1 upper bead and 5 lower beads, the other with 1 upper bead with 4 lower beads, when they learn soroban in school!

The size of beads of soroban is standardized, the Japanese classified soroban for native Japanese and foreigners, as Western people are of bigger body build and hands/fingers. The soroban that are for foreigners (Westerners) are made with a plastic pipe on both the left and right side of the frame, while ones made for native Japanese were all made with wooden frames. In this way the "thickness" of the soroban (for foreigners) is higher, rendering it easier for the non-Japanese to manipulate.

## Russian abacus

The Russian abacus, the schoty or sjotty (счёты), usually has a single slanted deck, with ten beads on each wire (except one wire which has four, and acts as a separator or for fractions). This wire is usually near the user. The Russian abacus is often used vertically, with wires from left to right in the manner of a book. The wires are usually bowed to bulge upward in the center, in order to keep the beads pinned to either of the two sides. It is cleared when all the beads are moved to the right. During manipulation, beads are moved to the left. For easy viewing, the middle 2 beads on each wire (the 5th and 6th bead) usually have a colour different to the other 8 beads. Likewise, the left bead of the thousands wire (and the million wire, if present) may have a different color.

The Russian abacus is still in common use today in shops and markets throughout the former Soviet Union, although it is no longer taught in most schools.

## School abacus

Around the World, abaci have been used in elementary schools as an aid in teaching arithmetics.
In Western countries, a model similar to the Russian abacus and often known as a **bead frame** has been common (see image).

## Uses by the visually impaired

Abaci are still used by individuals who have visual impairments. They use an abacus to perform the mathematical functions multiplication, division, addition, subtraction, square root and cubic root. A piece of soft fabric is placed behind the beads so that they don't move inadvertently. This keeps the beads in place while a person feels the beads or uses the abacus.

## Native American abacus

Some sources mention the use of an abacus called a *Nepohualtzintzin* in ancient Mayan culture. This Mesoamerican abacus uses the 5-digit base-20 Mayan numeral system.

The khipu of the Inkas was a system of knotted cords used to record numerical data - like advanced tally sticks—but was not used to perform calculations.

## See also

- Slide rule
- Napier's bones
- History of computing
- History of computing hardware
- Abacus logic
- Mental abacus
- Positional notation

## External links

- Abacus in Various Number Systems
- Soroban in Various Number Systems
- Suan pan in Various Number Systems
- Abacus
- Abacus: Mystery of the Bead - An Abacus Manual
- Advanced Abacus Techniques
- Lee Kai-chen's Improved Abacus
- Soroban
- Soroban Abacus Handbook A guide to addition, subtraction, multiplication and division.
- Soroban: The Japanese Abacus Soroban direct from Japan.
- Suan Pan
- Webarchive backup: Mesoamerican abacus (this site is no longer online - but the webarchive backup is; however, one of the author’s documents comparing the organization and use of the Mesoamerican abacus and the Chinese abacus is mirrored at [1]); see also [2]
- Roman abacus
- Abacus Photos and Images
- The World’s Smallest Abacus
- Java applet of Chinese, Japanese and Russian abaci

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