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# Abacus

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 numeral system and is still widely used by merchants and clerks in Russia, China and elsewhere.

## Roman abacus

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The Late Roman abacus shown here 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. The short grooves on the right may have been used for marking Roman ounces.

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

## Chinese abacus

The swanpan (算盤 or 筭盤 Pinyin: suan4 pan2) 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. 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 swanpan techniques have been developed to do multiplication, division, addition, subtraction, square root and cube root operations at high speed.

There are two types of beads on the abacus, those in the lower deck, below the separator beam, and those in the upper deck above it. The ones in the lower deck are sometimes called earth beads, and carry a value of 1 in their column. The ones in the upper deck are sometimes called heaven beads. The columns are much like the places in arabic numerals: one of the columns, usually the rightmost, represents the ones place; to the left it are the tens, hundreds, thousands place, and so on, and if there are any columns to the right of it, they are the tenths place, hundredths place, and so on.

At the end of a calculation on a Chinese abacus, it is never the case that all five beads in the lower deck are moved up; in this case, the five beads are pushed back down and one carry bead in the top deck takes their place. Similarly, if two beads in the top deck are pushed down, they are pushed back up, and one carry bead in the lower deck of the next column to the left is moved up. The result of the computation is read off from the beads clustered near the separator beam between the upper and lower deck.

The beads and rods are often lubricated to ensure quick, smooth motion.

### Decimal system

Like the Roman abacus, this device works as a bi-quinary 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, another abacus can be added to the left of the first. In theory, the abacus can be expanded indefinitely in this way.

### Modern decline in use

As recently as the late 1960s, abacus arithmetic was still being taught in school in Hong Kong and into the 1990s in Taiwan. However, when handheld calculators became readily available, 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 (Early electronic calculators could only handle 8 to 10 significant digits, whereas the abacus is virtually limitless in precision.) But when the functionality of calculators improved beyond simple arithmetic operations, most people realized that the abacus could never compute higher functions – such as those in trigonometry – faster than a calculator. Nowadays, as calculators have become more affordable, the abacus is hardly seen in Hong Kong. Abaci are, however, still being used elsewhere in China and in Japan. Though abaci are not commonly used in Hong Kong and Taiwan, many parents still send their children to private tutor to learn abacus as a learning aid and stepping stones to faster and more accurate mental arithmetic skills.

## 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 (算盤) more like the Roman abacus. The 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 double cones for easier flicking.

## Russian abacus

The Russian abacus usually has a single deck, with ten beads on each wire (except one wire which has fewer, and acts as a separator). It is often used vertically, in the manner of a book. It may also have a number of binary fields.

## 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.

Other less well-known uses of this word include abacus architecture and abacus logic.

Gnumeric is intended to be a replacement for a commercial spreadsheet. Part of the Gnome project.
http://www.gnome.org/gnumeric/