{{otheruses}}
An '''abacus''' (plurals '''abacuses''' or '''abaci'''), also called a '''counting frame''', is a calculating tool for performing arithmetic processes. Nowadays, abaci are often constructed as a wooden frame with beads sliding on wires, but originally they were beads or stones moved in grooves in sand or on tablets of wood, stone, or metal. The abacus was in use centuries before the adoption of the written [[Hindu-Arabic numeral system|modern numeral system]] and is still widely used by merchants and clerks in [[China]], [[Japan]], [[Africa]] and elsewhere.

The user of an abacus is called an '''abacist'''; he or she slides the beads of the abacus by hand.<ref> "abacist", "abacus", in Merriam-Webster's Third New International Dictionary Unabridged, 2000, Version 2.5.</ref>
[[Image:Boulier1.JPG|right|thumb|A Chinese abacus]]

==Origins==
The first abacus was almost certainly based on a flat stone covered with sand or dust. Words and letters were drawn in the sand; eventually numbers were added<ref>[http://search.eb.com/eb/article-9003215 "abacus."] ''[[Encyclopædia Britannica]]''. 3 February 2007</ref> and pebbles used to aid calculations. The [[Babylonians]] used this dust abacus as early as [[2400 BC]].<ref>Reilly, page 825</ref> The origin of the counter abacus with strings is obscure, but [[India]], [[Mesopotamia]] or [[Egypt]] are seen as probable points of origin.<ref>Smith, page 159</ref> [[China]] played an essential part in the development and evolution of the abacus.

From this, a variety of abaci were developed; the most popular were based on the [[Bi-quinary coded decimal|bi-quinary system]], using a combination of two bases (base-2 and base-5) to represent decimal numbers. But the earliest abaci used first in Mesopotamia and later by scribes in Egypt and Greece used [[sexagesimal]] numbers represented with factors of 5, 2, 3, and 2 for each digit.

The use of the word ''abacus'' dates from 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 language|Greek]] [[Genitive case|genitive form]] of ''abax'' ("calculating-table"). Because ''abax'' also had the sense of "table sprinkled with sand or dust, used for drawing geometric figures", some linguists speculate that the Greek word may be derived from a [[Semitic languages|Semitic]] [[Root (philology)|root]] (cf. [[Phoenician language|Phoenician]] ''abak'', "sand", [[Hebrew language|Hebrew]] ''ābāq'' (pronounced "a-vak"), "dust").{{Fact|date=January 2008}} The preferred plural of ''abacus'' is a subject of disagreement, but both ''abacuses''<ref>Oxford English Dictionary, 1989</ref> and ''abaci''<ref>Merriam-Webster's 2003</ref> are in use.

==Babylonian abacus==
Babylonians may have used the abacus for the operations of addition and subtraction. However, this primitive device proved difficult to use for more complex calculations.<ref>Carruccio, page 14</ref> Some scholars point to a character from the Babylonian cuniform which may have been derived from a representation of the abacus.<ref>Crump, page 188</ref>

==Egyptian abacus==
The use of the abacus in [[ancient Egypt]] is mentioned by the Greek historian [[Herodotus]], who writes that the manner of his disks usage by the Egyptians was opposite in direction when compared with the Greek method. Archaeologists have found ancient disks of various sizes that are thought to have been used as counters. However, wall depictions of this instrument have not been discovered, casting some doubt over the extent to which this instrument was used.<ref name=Smith1>Smith, page 160</ref>

==Greek abacus==
A tablet found on the Greek island [[Salamis Island|Salamis]] in 1846 dates back to 300 BC, making it the oldest counting board discovered so far. It is a slab of white marble 149 cm long, 75 cm wide, and 4.5 cm thick, on which are 5 groups of markings. In the center of the tablet is a set of 5 parallel lines equally divided by a vertical line, capped with a semi-circle at the intersection of the bottom-most horizontal line and the single vertical line. Below these lines is a wide space with a horizontal crack dividing it. Below this crack is another group of eleven parallel lines, again divided into two sections by a line perpendicular to them, but with the semi-circle at the top of the intersection; the third, sixth and ninth of these lines are marked with a cross where they intersect with the vertical line.

==Roman abacus==
[[Image:RomanAbacusRecon.jpg|right|thumb|250px|Reconstructed Roman Abacus]]
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{{Main|Roman abacus}}
The normal method of calculation in ancient Rome, as in Greece, was by moving counters on a smooth table. Originally pebbles, [[calculi]], were used. Later, and in medieval Europe, [[jeton]]s were manufactured. Marked lines indicated units, fives, tens etc. as in the [[Roman numeral]] system. This system of 'counter casting' continued into the late Roman empire and in medieval Europe, and persisted in limited use into the nineteenth century.<ref>Pullan, page 18</ref>

In addition to the more common method using loose counters, several specimens have been found of a [[Roman abacus]], shown here in reconstruction. It has eight long grooves containing up to five beads in each and eight shorter grooves having either one or no beads in each.

The groove marked I indicates units, X tens, and so on up to millions. The beads in the shorter grooves denote fives&mdash;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.

==Indian abacus==
[[1st century]] sources, such as the ''Abhidharmakosa'' describe the knowledge and use of abacus in [[India]].<ref>Stearns, page 44</ref> Around the [[5th century]], Indian clerks were already finding new ways of recording the contents of the Abacus.<ref>Körner, page 232</ref> Hindu texts used the term ''shunya''(means Zero) to indicate the empty column on the abacus.<ref>Mollin, page 3</ref>

==Chinese abacus==
[[Image:abacus 6.png|thumb|Suanpan (the number represented in the picture is 6,302,715,408)]]
{{Main|Suanpan}}
The earliest mention of a suanpan is found in a First Century book of the [[Eastern Han Dynasty]], namely ''Supplementary Notes on the Art of Figures'' written by Xu Yue.<ref>Peng Yoke Ho, page 71</ref> However, the exact design of this suanpan is not known.

Usually, a suanpan is about 20 cm tall and it comes in various widths depending on the operator. 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. Modern abacuses have one bead on the top deck and four beads on the bottom deck. The beads are usually rounded and made of a [[hardwood]]. The beads are counted by moving them up or down towards the beam. If you move them high, you count their value. If you move them down, you don't count their value. The suanpan 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.

Suanpans 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 (mathematics)|division]], [[addition]], [[subtraction]], [[square root]] and [[cube root]] operations at high speed.

In the famous long scroll ''[[Zhang Zeduan#The Qingming Scroll|Riverside Scenes at Qingming Festival]]'' painted by [[Zhang Zeduan]] ([[1085]]-[[1145]]) during the [[Song Dynasty]] ([[960]]-[[1297]]), a suanpan is clearly seen lying beside an account book and doctor's prescriptions on the counter of an [[apothecary]]'s (Feibao).

The similarity of the [[Roman abacus]] to the Chinese one suggests that one could have inspired the other, as there is some evidence of a trade relationship between the [[Roman Empire]] and China. However, no direct connection can be demonstrated, and the similarity of the abaci may be coincidental, both ultimately arising from counting with five fingers per hand. Where the Roman model (like most modern [[Abacus#Japanese abacus|Japanese]]) has 4 plus 1 bead per decimal place, the standard suanpan has 5 plus 2, allowing less challenging arithmetic algorithms, and also allowing use with a [[hexadecimal]] numeral system. Instead of running on wires as in the Chinese and Japanese models, the beads of Roman model run in groves, presumably making arithmetic calculations much slower.

Another possible source of the suanpan is Chinese [[counting rods]], which operated with a [[decimal system]] but lacked the concept of [[0 (number)|zero]] as a place holder. The zero was probably introduced to the Chinese in the [[Tang Dynasty]] (618-907) when travel in the [[Indian Ocean]] and the [[Middle East]] would have provided direct contact with [[India]] and [[Islam]] allowing them to acquire the concept of zero and the [[decimal point]] from Indian and Islamic merchants and mathematicians.

==Japanese abacus==
[[Image:Soroban.JPG|thumb|right|400px|Japanese soroban]]
{{main|Soroban}}
A '''soroban''' ({{lang|ja|算盤, そろばん}}, lit. "Counting tray") is a Japanese-modified version of the Chinese abacus. It is devised from the suanpan, imported from China to Japan through the [[Korean peninsula]] in the [[15th century]]. Like the suanpan, the soroban is still used in Japan today, even with the proliferation, practicality, and affordability of pocket electronic calculators.

Korea also has its own called the '''supan''' (수판), which is basically the soroban before it took its modern form in the 1930s. The modern soroban also goes by this Korean name.<ref>This term is used extensively in the Korean website http://www.supan.net, which not only offers lessons on using the abacus but also sells soroban, particularly from Japanese dealer Tomoe.</ref>

==Native American abaci==
[[Image:Quipu.png|thumb|100px|Representation of an [[Inca]] [[quipu]]]]
{{Unreferencedsection|date=October 2007}}
Some sources mention the use of an abacus called a '''''nepohualtzintzin''''' in ancient Aztec culture. This Mesoamerican abacus used a 5-digit base-20 system.

The [[quipu]] of the [[Inca]]s was a system of knotted cords used to record numerical data, like advanced [[tally stick]]s&mdash;but not used to perform calculations. Calculations were carried out using a [[yupana]] ([[quechua]] for "counting tool"; see figure) which was still in use after the conquest of Peru. The working principle of a yupana is unknown, but in 2001 an explanation of the mathematical basis of these instruments was proposed. By comparing the form of several yupanas, researchers found that calculations were based using the [[Fibonacci sequence]] 1,1,2,3,5 and powers of 10, 20 and 40 as place values for the different fields in the instrument. Using the Fibonacci sequence would keep the number of grains within any one field at minimum.
{{-}}

==Russian abacus==
[[Image:Schoty abacus.jpg|thumb|Russian abacus]]
The Russian abacus, the ''schoty'' (счёты), usually has a single slanted deck, with ten beads on each wire (except one wire which has four beads, for quarter-ruble fractions). This wire is usually near the user. (Older models have another 4-bead wire for quarter-kopeks, which were minted until 1916.) 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 from 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 use today in shops and markets throughout the [[Commonwealth of Independent States|former Soviet Union]], although it is no longer taught in most schools.

==School abacus==
[[Image:Kugleramme.jpg|left|150px|thumb|School abacus used in Danish elementary school. Early 20th century.]]

Around the world, abaci have been used in pre-schools and elementary schools as an aid in teaching the [[numeral system]] and [[arithmetic]]. In Western countries, a '''bead frame''' similar to the Russian abacus but with straight wires and a vertical frame has been common (see image). It is still often seen as a plastic or wooden toy.

The type of abacus shown here is often used to represent numbers without the use of place value. Each bead and each wire has the same value and used in this way it can represent numbers up to 100.

The most significant educational advantage of using an abacus, rather than loose beads or counters, when practicing counting and simple addition is that it gives the student an awareness of the groupings of 10 which are the foundation of our number system. Although adults take this base 10 structure for granted, it is actually difficult to learn. Many 6-year-olds can count to 100 by rote with only a slight awareness of the patterns involved.

==Uses by the blind==
An adapted abacus, called a Cranmer abacus is still commonly used by individuals who are [[blindness|blind]]. A piece of soft fabric or rubber is placed behind the beads so that they do not move inadvertently. This keeps the beads in place while the users feel or manipulate them. They use an abacus to perform the mathematical functions [[multiplication]], [[division (mathematics)|division]], [[addition]], [[subtraction]], [[square root]] and [[cubic root]].

Although blind students have benefited from talking calculators, the abacus is still very often taught to these students in early grades, both in public schools and state schools for the blind. The abacus teaches math skills that can never be replaced with talking calculators and is an important learning tool for blind students. Blind students also complete math assignments using a braille-writer and [[Nemeth Braille|Nemeth code]] (a type of braille code for math) but large multiplication and long division problems can be long and difficult. The abacus gives blind and visually impaired students a tool to compute math problems that equals the speed and mathematical knowledge required by their sighted peers using pencil and paper. Many blind people find this number machine a very useful tool throughout life.

==Notes==
{{reflist|2}}

==References==

*{{cite book
| last = Reilly
| first = Edwin D.
| coauthors = William Leonard Langer
| title = Concise Encyclopedia of Computer Science
| publisher = John Wiley and Sons
|date=2004
| isbn = ISBN 0470090952}}

*{{cite book
| last = Körner
| first = Thomas William
| coauthors = William Leonard Langer
| title = The Pleasures of Counting
| publisher = Houghton Mifflin Books
|date=1996
| isbn = ISBN 0521568234}}

*{{cite book
| last = Mollin
| first = Richard Anthony
| title = Fundamental Number Theory with Applications
| publisher = [[CRC Press]]
|date=1998
| month = September
| isbn = ISBN 0849339871 }}

*{{cite book
| last = Smith
| first = David Eugene
| title = History of Mathematics (Volume 2)
| publisher = Courier Dover Publications
| isbn = ISBN 0486204308 }}

*{{cite book
| last = Crump
| first = Thomas
| title = The Japanese Numbers Game: The Use and Understanding of Numbers in Modern Japan
| publisher = Routledge
|date=1992
| isbn = ISBN 0415056098}}

*{{cite book
| last = Carruccio
| first = Ettore
| title = Mathematics And Logic in History And in Contemporary Thought
| publisher = Aldine Transaction
|date=2006
| isbn = ISBN 0202308502}}

*{{cite book
| last = Stearns
| first = Peter N.
| coauthors = William Leonard Langer
| title = The Encyclopedia of World History: Ancient, Medieval, and Modern, Chronologically Arranged
| publisher = Houghton Mifflin Books
|date=2001
| isbn = ISBN 0395652375}}

*{{cite book
| author = Peng Yoke Ho
| title = Li, Qi and Shu: An Introduction to Science and Civilization in China
| publisher = Courier Dover Publications
|date=2000
| isbn = ISBN 0486414450}}

*{{Cite book
| publisher = Merriam-Webster, Inc
| isbn = 0877798095
| title = Merriam-Webster's Collegiate Dictionary
|date=2003
| edition = 11th edtion
}}

*{{OED|abacus}}

*{{cite book
| last = Pullan
| first = J. M.
| year = 1968
| title = The History of the Abacus
| publisher = Books That Matter
| location = London
| isbn=0-09-089410-3
}}

==See also==
* [[Abacus logic]]
* [[Abacus system]]
* [[Chisanbop]]
* [[Napier's bones]]
* [[Sand table]]

==Further reading==
*{{cite book
| last = Menninger
| first = Karl W.
| year = 1969
| title = Number Words and Number Symbols: A Cultural History of Numbers
| publisher = MIT Press
| isbn=0-262-13040-8
}}
*{{cite book
| last = Kojima
| first = Takashi
| year = 1954
| title = The Japanese Abacus: its Use and Theory
| publisher = Charles E. Tuttle
| location = Tokyo
| isbn=0-8048-0278-5
}}

==External links==
{{sisterlinks}}
===Tutorials===
<!-- in alphabetical order by author -->
* [http://www.minmm.com/minc/show_classes.php?id=273 Min Multimedia]
* [http://www.sungwh.freeserve.co.uk/sapienti/abacus01.htm Suan Pan]
* [http://webhome.idirect.com/~totton/abacus/ Abacus: Mystery of the Bead - an Abacus Manual]

===Abacus curiosities===
* [http://sks23cu.net/TSA/ The Stephenson Abacus™], by Steve Stephenson
* [http://www.cut-the-knot.org/blue/Abacus.shtml Abacus in Various Number Systems] at [[cut-the-knot]]
* [http://www.tux.org/~bagleyd/abacus.html Java applet of Chinese, Japanese and Russian abaci]
* [http://www.research.ibm.com/atomic/nano/roomtemp.html An atomic-scale abacus]
* [http://www.ee.ryerson.ca/~elf/abacus/ History of the abacus and more]
* [http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=1187&bodyId=1328 Gerbert d'Aurillac's abacus using Hindu-Arabic numerals] at [http://mathdl.maa.org/convergence/1/ Convergence]
* [http://demonstrations.wolfram.com/Abacus/ "Abacus"] by Michael Schreiber, [[The Wolfram Demonstrations Project]], 2007.

[[Category:Roman mathematics]]
[[Category:Mechanical calculators]]

[[af:Abakus]]
[[ar:أباكوس]]
[[ay:Jakhuña]]
[[bn:অ্যাবাকাস]]
[[be-x-old:Абак]]
[[ca:Àbac]]
[[cs:Abakus (kalkulátor)]]
[[da:Abacus (regnemaskine)]]
[[de:Abakus (Rechentafel)]]
[[et:Abakus]]
[[el:Άβακας]]
[[es:Ábaco]]
[[eo:Abako (meĥanika kalkulilo)]]
[[eu:Abako]]
[[fa:چرتکه]]
[[fr:Boulier]]
[[gl:Ábaco]]
[[ko:수판]]
[[id:Sempoa]]
[[ia:Abaco]]
[[it:Abaco]]
[[he:חשבונייה]]
[[lo:ລູກຄິດ]]
[[lt:Abakas]]
[[hu:Abakusz]]
[[nah:Nepōhualtzintzin]]
[[nl:Abacus (rekentuig)]]
[[ja:そろばん]]
[[no:Abakus (kuleramme)]]
[[nn:Kuleramme]]
[[pl:Abakus (liczydło)]]
[[pt:Ábaco]]
[[ro:Abac]]
[[ru:Абак (математика)]]
[[scn:Badduttuleri]]
[[simple:Abacus]]
[[sk:Abakus (počítacia tabuľka)]]
[[sl:Abak]]
[[sr:Абакус (рачунање)]]
[[fi:Helmitaulu]]
[[sv:Abakus]]
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[[ta:எண்சட்டம்]]
[[th:ลูกคิด]]
[[tr:Sayı boncuğu]]
[[uk:Абак]]
[[ur:گنتارا]]
[[zh-yue:算盤]]
[[zh:算盘]]