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# Abacus

See also abacus (architecture) – a flat slab at the top of a column.

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.

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## 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. 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

The suanpan (算盤 or 筭盤 Pinyin: suànpán) 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.

## 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 when used in decimal system. 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 a double cone to facilitate ease of movement.

Japanese soroban

## 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.

## Native American abacus

Some sources also mention the use of the abacus in ancient Mayan culture. The Mesoamerican abacus uses the 5-digit base-20 Mayan numeral system.

## Uses by the visually impaired

Abaci are still used by individuals who have visual impairment s. 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.

• Abacus in Various Number Systems http://www.cut-the-knot.org/blue/Abacus.shtml
• Soroban in Various Number Systems http://www.cut-the-knot.org/Curriculum/Arithmetic/Soroban.shtml
• Suan pan in Various Number Systems http://www.cut-the-knot.org/Curriculum/Arithmetic/SuanPan.shtml
• Abacus http://www.ee.ryerson.ca/~elf/abacus/
• Soroban http://www.soroban.com/
• Soroban Abacus Handbook http://www.gis.net/~daveber/Abacus/Abacus.htm A guide to addition, subtraction, multiplication and division.
• Suan Pan http://www.sungwh.freeserve.co.uk/sapienti/abacus01.htm
• Webarchive backup: Mesoamerican abacus http://web.archive.org/web/20011202050525/hawk.hama-med.ac.jp/dbk/abacus.html (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] http://www.ee.ryerson.ca/~elf/abacus/dbk/ ); see also [2] http://www.peterassociates.com/mayan-abacus.htm
• Roman abacus http://www.dotpoint.com/xnumber/pic_roman_abacus.htm
• Abacus Photos and Images http://www.abacus.ca/abacus-images.php
• The World’s Smallest Abacus http://www.research.ibm.com/atomic/nano/roomtemp.html
• Java applet of Chinese, Japanese and Russian abaci http://www.tux.org/~bagleyd/abacus.html

Last updated: 02-07-2005 15:37:50