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Abacus

2007 Schools Wikipedia Selection. Related subjects: Everyday life;
Mathematics

   An abacus (plurals abacuses or abaci) is a calculating tool, often
   constructed as a wooden frame with beads sliding on wires. It was in
   use centuries before the adoption of the written Hindu-Arabic numeral
   system and is still widely used by merchants and clerks in China,
   Japan, Africa and elsewhere.
   A Chinese abacus
   A Chinese abacus

Origins

   The origins of the abacus are disputed; many cultures are known to have
   used similar tools. It is known to have first existed in Mesopotamia
   and China, and was invented sometime between 1000 BC and 500 BC. 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 and pebbles used to aid calculations. From this, a
   variety of abaci were developed; the most popular were based on the
   bi-quinary system, using a combination of two bases (base-2 and base-5)
   to represent decimal numbers.

   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 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
   root, ābāq, the Hebrew word for "dust". Though details of the
   transmission are obscure, it may also be derived from the Phoenician
   word abak, meaning "sand". The plural of abacus is often subject to
   heated debate. The equivocal American dictionary cites the plural as
   abaci with reference to similar usage with the words Cactus and Fungus.
   However the equivocal British dictionary cites the plural as abacuses
   due to the word's Arabic origin.

Greek abacus

   A tablet found on the Greek island Salamis in 1846 dates back to 300 BC
   making it the oldest counting board discovered so far. It was
   originally thought to be a gaming board. Its construction is a slab of
   white marble measuring 149 cm in length, 75 cm in width and 4.5 cm
   thick, on which are 5 groups of markings. In the centre of the tablet
   are 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

   Reconstructed Roman Abacus
   Reconstructed Roman Abacus

   The Late Empire Roman abacus shown here in reconstruction contains
   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—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.

Chinese abacus

   Before the invention of the Chinese abacus, counting rods, other
   symbolic methods such as tally sticks, notches on bones, and the like,
   were undoubtedly used as a tool for counting and calculation.

   The suanpan ( Simplified Chinese: 算盘; Traditional Chinese: 算盤; Hanyu
   Pinyin: suànpán, lit. "Counting tray") of the Chinese is similar to the
   Roman abacus in principle, though has a different construction, and it
   was designed to do both decimal and hexadecimal arithmetics.
   Chinese abacus, the suanpan

   The Chinese abacus is typically around 20 cm (8 inches) tall and it
   comes in various widths, depending on the application and hand size of
   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. 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 centre.
   A Chinese bookkeeper using an abacus to calculate his accounts
   A Chinese bookkeeper using an abacus to calculate his accounts

   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.

   Bead arithmetic ( Simplified Chinese: 珠算; Traditional Chinese: 珠算;
   Hanyu Pinyin: chùsuàn) is the calculating technique used with various
   types of abaci, in particular the Chinese abacus. 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. The
   standard Chinese abacus has 5 beads plus 2 for decimals, allows for
   more challenging arithmetic algorithms than the Roman model, and also
   allows for use with a hexadecimal numeral system.

Japanese abacus

   Japanese soroban
   Japanese soroban

   Soroban (算盤, lit. "Counting tray") is a Japanese-modified version of
   the Chinese abacus (算盤). The Japanese first eliminated one bead from
   the upper deck and later another bead from the lower deck in each
   column of the Chinese abacus, making the Japanese abacus purely for the
   decimal system. The Japanese also eliminated the use of the Qiuchu
   (Chinese division table). However, the Chinese division table was still
   used when there were 5 lower beads. There came the debate of the
   multiplication table versus the division table, with the school of
   multiplication table prevailing in the 1920s. The rods (number of
   digits) usually increase to 21, 23, 27 or even 31, thus allowing
   calculation for more digits or representations of several different
   numbers at the same time. On November 12, 1946 a contest between the
   Japanese soroban and an electric calculator was held in Tokyo. The
   soroban won 4 to 1.

   Soroban is taught in primary schools as a part of lessons in
   mathematics because the decimal numerical system can be demonstrated
   visually. When teaching the soroban, a song-like instruction is given
   by the teacher. The soroban is about 8 cm (3 inches) tall. The beads on
   a soroban are usually shaped as a double cone (bi-cone) to facilitate
   ease of movement. Often, primary school students may bring along with
   them two sorobans, one with 1 upper bead and 5 lower beads, the other
   with 1 upper bead with 4 lower beads. Despite the advent of handheld
   calculators, some parents send their children to private tutors to
   learn soroban because proficiency in soroban calculation can be easily
   converted to mental arithmetic at a highly advanced level.

Russian abacus

   Russian abacus
   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 colour.

   The Russian abacus is still in use today in shops and markets
   throughout the former Soviet Union, although it is no longer taught in
   most schools.

School abacus

   School abacus used in Danish elementary school. Early 20th century.
   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 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 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 user feels or manipulates them. They use an
   abacus to perform the mathematical functions multiplication, 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 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.

Native American abaci

   Representation of an Inca quipu
   Representation of an Inca quipu

   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 has
   been proposed: comparing the form of several yupanas, it appears 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.
   Retrieved from " http://en.wikipedia.org/wiki/Abacus"
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   with only minor checks and changes (see www.wikipedia.org for details
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