A Brief Introduction to the Abacus
Anatomy & Construction
The standard abacus can be used to perform addition, subtraction, division
and multiplication; the abacus can also be used to extract square-roots
and cubic roots.
The abacus is typically constructed of various types of hardwoods and comes in varying sizes. The frame of the abacus has a series of vertical rods on which a number of wooden beads are allowed to slide freely. A horizontal beam separates the frame into two sections, known as the upper deck and the lower deck.
Abacus Parts: The various parts of the abacus are identified here: the frame, the beam, the beads and rods and the upper and lower decks.
Basics
The abacus is prepared for use by placing it flat on a table or one's lap
and pushing all the beads on both the upper and lower decks away from the
beam. The beads are manipulated with either the index finger or the thumb
of one hand.
Bead Values
Each bead in the upper deck has a value of 5; each bead in the lower deck
has a value of 1. Beads are considered counted, when moved towards the beam
that separates the two decks.
Counting
After 5 beads are counted in the lower deck, the result is "carried"
to the upper deck; after both beads in the upper deck are counted, the result
(10) is then carried to the left-most adjacent column.
The right-most column is the ones column; the next adjacent to the left
is the tens column; the next adjacent to the left is the hundreds column,
and so on. Floating point calculations are performed by designating a space
between 2 columns as the decimal-point and all the rows to the right of
that space represent fractional portions while all the rows to the left
represent whole number digits.
Technique
Proper finger technique is paramount in achieving proficiency on the abacus.
With a Chinese abacus, the thumb and the index finger together with the
middle finger are used to manipulate the beads. Beads in lower deck are
moved up with the thumb and down with the index finger. In certain calculations,
the middle finger is used to move beads in the upper deck.
Finger Technique: A Japanese textbook published in 1954 shows the proper technique for moving the beads. It shows the thumb being used to count beads in the lower deck and the index finger being used in all other cases.
With the Japanese version, only the index finger and thumb are used. The
beads are moved up with the thumb and down with the index finger. However,
certain complex operations require that the index finger move beads up;
e.g. adding 3 to 8 (the adding of the three is called Jian Chi Jia Shi which
literally means, "subtract 7 add 10").
This Java version of the abacus is a limited simulation of the real device
because the fingering technique is completely obfuscated by the mouse. With
a real abacus, constant practice is indispensable in achieving virtuosity
and calculating speed.
The Abacus Today
A store clerk in Beijing, China uses the abacus to
settle accounts.
The abacus is still in use today by shopkeepers in Asia and "Chinatowns"
in North America. The use of the abacus is still taught in Asian schools,
and some few schools in the West. Blind children are taught to use the abacus
where their sighted counterparts would be taught to use paper and pencil
to perform calculations.
One particular use for the abacus is teaching children simple mathematics
and especially multiplication; the abacus is an excellent substitute for
rote memorization of multiplication tables, a particularily detestable task
for young children. The abacus is also an excellent tool for teaching other
base numbering systems since it easily