E N C Y C L O P E D I A

Abacus

An abacus is a counting frame, typically wooden with balls sliding on wires. It was first used before the adoption of the ten-digit Arabic numeral system and is still widely used by small merchants in China.

Table of contents

1 Roman abacus
2 Chinese abacus

2.1 Beads
2.2 Decimal system
2.3 Modern decline in use
2.4 Miscellanea

3 Japanese abacus
4 Native American abacus

Roman abacus

The Roman abacus contains seven long and seven shorter rods or bars, the former having four perforated beads running on them and the latter one. This figure of a Roman abacus is taken from an ancient monument:

The bar marked 1 indicates units, X tens, and so on up to millions. The beads on the shorter bars denote fives,--five units, five tens, etc. The rod O and corresponding short rod are for marking ounces; and the short quarter rods for fractions of an ounce. Computations are made with it by means of balls of bone or ivory running on slender bamboo rods, similar to the simpler board, fitted up with beads strung on wires, which has been employed in teaching the rudiments of arithmetic in English schools.

Chinese abacus

The swanpan (算盤 or 筭盤 Pinyin: suan4 pan2) of the Chinese closely resembles the Roman abacus in its construction and use.

The Chinese abacus is usually around 20 cm (8 inches) tall and it comes in various width depending on 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. The beads are usually round and made of hard wood. 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. The beads are counted by moving them up or down towards the beam.

Chinese abaci haze functions other than counting. Unlike the simple counting board used in elementary schools, very efficient suanpan techniques were developed to do multiplication, division, addition, subtraction, square root and cubic root operations at high speed.

Beads

The beads and rods were often lubricated to ensure speed. When all five beads in the lower deck are moved up, they are reset to the original position, and one bead in the top deck is moved down as a carry. When both beads in the upper deck are moved down, they are reset and a bead on the adjacent rod on the left is moved up as a carry. The result of the computation is read off from the beads clustered near the separator beam between the upper and lower deck.

Decimal system

In a sense, the abacus works as a 5-2-5-2 based number system in which carries and shiftings are similar to the decimal number system. Since each rod represents a digit in a decimal number, the computation capacity of the abacus is only limited by the number of rods on the abacus. When a mathematician runs out of rods, he simply adds another abacus to the left of the row. In theory, the abacus can be expanded infinitely.

Modern decline in use

As recently as the late 1960s, abacus arithmetic was still being taught in school, as in Hong Kong; and into the 1990s in Taiwan. When handheld calculators became popular, schoolchildren's willingness to learn the use of the abacus decreased dramatically. In the early days of handheld calculators, news of abacus operators beating electronic calculators in arithmetic competitions in both speed and accuracy often appeared in the media. The reason for this was that early electronic calculators were often plagued by rounding and overflow errors. While most handheld calculators can only handle 8 to 10 significant digits, the abacus is virtually limitless in precision. Inexperienced operators might contribute to the loss too. But when the functionality of calculators improved, most Chinese realized that the abacus could never compute higher functions -- such as those in trigonometry -- faster than a calculator. The older generation -- mostly those who were born before the early 1950s -- still used the abacus for a while, but electronic calculators have gradually displaced the abacus in Hong Kong over the past four decades. Nowadays, as calculators have become more affordable, the abacus is hardly seen in Hong Kong. Abaci are, however, still being used in China and Japan. The slide rule has also suffered a similar demise.

Miscellanea

The swanpan is closely tied to the Chinese "Hua1 Ma3" numbering system.

Japanese abacus

The Japanese eliminated one bead each from the upper and lower deck in each column of the Chinese abacus, because these beads are redundant. That makes the Japanese soroban (十露盤) more like the Roman abacus. The soroban is about 8 cm (3 inches) tall. The beans on a soroban are usually double cone shape.

Native American abacus

Many sources also mentioned use of abacus in ancient Mayan culture. The Mesoamerican abacus is closely tied to the base-20 Mayan numerals system.

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.