1. Dust Abacus |
The original utilization of an abacus-related calculation system is presumed to
have been in the form of a board covered with dust or fine sand. The sand
was divided into lines, each one representing a different numerical
position. Numbers and quantities were calculated by means of various signs
drawn along the lines. The early civilization of Mesopotamia may have seen
the development of such a rudimentary calculator. |
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2. Line Abacus |
With time, the dust abacus developed into a ruled board on which pebbles or counters
were placed on lines somewhat like checkers on a backgammon board. Its wide use in
Egypt, Rome, Greece, India, and other ancient civilizations is well attested. Herodotus
(484-425 BC) most likely refers to a line abacus in his record: gThe Egyptians move their
hand from right to left in calculations, while the Greeks from left to right.h A famous
example of the line abacus is the Salamis Abacus preserved at the Athens Museum.
It consists of a white marble board (149 by 75 centimeters) with lines drawn on it. |
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3. Grooved Abacus |
In addition to the line abacus, the Romans made
use of a more advanced design. Several grooves were carved into
the board along which counters were moved up and down. One counter
was laid in each of the upper grooves, while four in each of
the lower grooves. Some additional counters were laid on the
right to facilitate the calculation of fractions. |
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Roman Grooved Abacus
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4. Ancient Chinese Abacus |
The early Chinese abacus was very similar to the ancient Roman grooved abacus.
The picture below represents the ancient Chinese abacus imagined from a description given
in a book titled Mathematical Treatises by Ancients written by Hsu Yo towards the end of
the Later Han Dynasty, about 1700 years ago, and annotated by Chen Luan some 300
years later. |
This abacus is closely similar to the Roman grooved abacus both in construction and in
the method of calculation. It may well be assumed that the Roman grooved abacus was
introduced to China in earlier days. |
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5. Chinese Abacus |
In China, the abacus came into common use during the Ming Dynasty. A book titled
Ch' o Ching Lu gives this proverbial expression: gA servant, some time after he is hired,
comes to do nothing more than he is ordered to. Therefore, he is like an abacus counter.h
A book written by Wu Ching-Hsin-Min in 1450 gives descriptions of the abacus.
A large number of books published towards the end of the Ming Dynasty attest to the fact
that the abacus had come into popular use. The abacus then had two counters above the bar
and five below. This type of abacus is still being used in China these days. |
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Ancient Chinese Abacus
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6. Soroban (Japanese Abacus) |
A little past the middle of the fifteenth century, the Chinese abacus
and its operational technique were introduced to Japan. Shortly afterward,
Japan entered a long period of peace, which fostered the development
of her cities and commerce. Mathematicians' constant and diligent
study developed a distinct Japanese method of the soroban operation
different from the original Chinese method. The large-sized Chinese
abacus was improved into a handier smaller-sized one. Towards the
end of the nineteenth century, the soroban with one five-unit counter
and four one-unit counters on each rod came into use along with the
older type which had one five-unit counter and five one- unit counters
on each rod. In 1938, the technique of the soroban operation was included
in the national grade-school textbooks on arithmetic compiled by the
Education Ministry. Today, the soroban technique is a required study
in the third and upper grades. The soroban with one five-unit counter
and four one-unit counters on each rod is the standard nowadays. It
should also be noted that the older Chinese division method, which
makes use of the cumbersome division table, was formerly replaced
by the Japanese division method, which makes use of the multiplication
table. The inclusion of the soroban technique in the curriculum of
Japanese compulsory education and the enforcement of the soroban efficiency
tests system since its inception in 1928 have been the two major factors
which have led to the present popularity of soroban in Japan.
Japanese Abacus (used
till the 19th century)
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Abacus (Soroban) for foreigner's use
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Current Abacus (Soroban) in Japan
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