• Finnish: abakus
• Polish: abakus, abak, liczydło
• Portuguese: ábaco
• Russian: абак

• Bosnian: računaljka
• Catalan: àbac
• Chinese:

  Mandarin: 算盤, 算盘 (suànpán)

• Danish: kugleramme
• Dutch: telraam, abacus
• Esperanto: abako
• Estonian: arvelaud
• Filipino: abakus, abako
• Finnish: helmitaulu
• French: abaque, boulier, boulier compteur
• German: Abakus, Rechenbrett
• Greek: άβακας (ávakas)
• Hebrew: חשבונייה (kheshboniya)
• Hindi: गिनतारा
• Hungarian: abakusz
• Icelandic: talnagrind
• Ido: abako
• Indonesian: sempoa
• Interlingua: abaco
• Irish: fráma comhairimh m4
• Italian: abaco
• Japanese: 算盤, そろばん
• Korean: 주판 (jupan)
• Malay: sempoa
• Malayalam: മണിച്ചട്ടം
• Maltese: abaku
• Persian: (chortkeh)
• Polish: liczydło, abakus
• Portuguese: ábaco
• Romanian: abac
• Russian: счёты
• Serbian:

  Cyrillic: рачунаљка

  Roman: računaljka

• Slovene: abak
• Spanish: ábaco
• Swedish: kulram, abakus
• Turkish: abaküs
• Vietnamese: bàn tính

Derived terms

• abacus harmonicus

Related terms

• abacist

References

• Webster 1913}}

Shorthand

• (Version: [[w:Gregg Shorthand#Centennial Gregg Shorthand sc=polytonic

Noun

1. a square board.
2. sideboard.
3. counting board.
4. gaming board.
5. panel.

Inflection

Descendants

• English: abacus
• French: abaque
• Italian: abaco
• Portuguese: ábaco
• Spanish: ábaco

References

Professor Kidd, et al. Collins Gem Latin Dictionary. HarperCollins Publishers (Glasgow: 2004). ISBN 0-00-470763-X. page 1.

An abacus, 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 modern numeral system and is still widely used by merchants and clerks in China, Japan, Africa, India and elsewhere.

The user of an abacus is called an abacist; he or she slides the beads of the abacus by hand.

Etymology

The use of the word abacus dates before 1387 AD, 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"), from Hebrew ābāq, "dust". The preferred plural of abacus is a subject of disagreement, but both abacuses and abaci are in use.

Mesopotamian abacus

The period 2700–2300 BC saw the first appearance of the Sumerian abacus, a table of successive columns which delimited the successive orders of magnitude of their sexagesimal number system.

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. Some scholars point to a character from the Babylonian cuneiform which may have been derived from a representation of the abacus.

Egyptian abacus

The use of the abacus in Ancient Egypt is mentioned by the Greek historian Crabertotous, who writes that the manner of this disk's 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..

Greek abacus

The earliest archaeological evidence for the use of the Greek abacus dates to the 5th century BC. The Greek abacus was a table of wood or marble, pre-set with small counters in wood or metal for mathematical calculations. This Greek abacus see use in Achaemenid Persia, the Etruscan civilization, Ancient Rome and, until the French Revolution, the Western Christian world.

A tablet found on the Greek island Salamis in 1846 AD 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

The earliest known written documentation of the Chinese abacus dates to the 14th century AD.

The Chinese abacus known as the suànpán is typically 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, addition, subtraction, square root and cube root operations at high speed.

In the famous long scroll Riverside Scenes at Qingming Festival painted by Zhang Zeduan (1085–1145 AD) during the Song Dynasty (960-1297 AD), 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 Japanese) has 4 plus 1 bead per decimal place, the standard suanpan has 5 plus 2, 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 grooves, 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 zero as a place holder. The zero was probably introduced to the Chinese in the Tang Dynasty (618-907 AD) when travel in the Indian Ocean and the Middle East would have provided direct contact with India, allowing them to acquire the concept of zero and the decimal point from Indian merchants and mathematicians.

The Chinese abacus migrated from China to Korea around the year 1400 AD. Koreans call it jupan (주판), supan (수판) or jusan (주산).

Indian abacus

1st century sources, such as the Abhidharmakosa describe the knowledge and use of abacus in India. Around the 5th century, Indian clerks were already finding new ways of recording the contents of the Abacus. Hindu texts used the term shunya(means Zero) to indicate the empty column on the abacus.

Japanese abacus

In Japanese, the abacus is called Soroban (, lit. "Counting tray") in Japan, imported via Korea around 1600. The 1/4 abacus appeared circa 1930, and it is preferred and still manufactured in Japan today even with the proliferation, practicality, and affordability of pocket electronic calculators. The use of the Soroban is still taught in Japanese primary schools as a part of math.

Korean abacus

The abacus migrated from China to Korea around the year 1400 AD. Korea's version of the abacus is called jupan (주판) or supan (수판) or jusan (주산).

Native American abacuses

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 Incas was a system of knotted cords used to record numerical data, like advanced tally sticks—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

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 was in use in all shops and markets throughout the former Soviet Union, and the usage of it was taught in most schools till 1990s. Today it is regarded as an archaism and replaced by microcalculator. The usage of calculators has been taught since the 1990s.

School abacus

|date=1998 | month = September | isbn = ISBN 0849339871 }}

See also

• Abacus logic
• Abacus system
• Chisanbop
• Napier's bones
• Sand table

Further reading

External links

Tutorials

• Min Multimedia

Abacus curiosities

• Abacus in Various Number Systems at cut-the-knot
• Java applet of Chinese, Japanese and Russian abaci
• An atomic-scale abacus

nah:Nepōhualtzintzin