The abacus is a calculator whose earliest known use is circa 500 B.C. by the Chinese civilization. Addition, subtraction, division and multiplication can be performed on a standard abacus. Beginning in about 1600 A.D., use and evolution of the abacus was begun by the Japanese. Archeological excavations have revealed an Aztec abacus, circa 900-1000 A.D., where the counters were made from kernels of maize threaded through a string that was attached to a wooden frame.
Construction & Anatomy
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 (at one time perhaps made of bamboo) 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.
FIGURE: The Anatomy of a Chinese Abacus.
The figure above identifies the various parts of a Chinese abacus. If your browser is Java-capable then the abacus applet (further down) will identify the various parts in your browser's status area as your mouse-pointer moves over it.
Basics
Calculations are performed by placing the abacus flat on a table or one's lap and manipulating the beads with the fingers of one hand.
Each bead in the upper deck has a value of five; each bead in the lower deck has a value of one.
Beads are considered counted, when moved towards the beam that separates the two decks.
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. 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. 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.
Since your browser does not support java, this image is a place holder for the applet.
FIGURE/APPLET: Numeric representation of the number: 87,654,321.
With reference to Figure/Applet above, the third column (from the left), representing the number 8, is composed of 1 bead from the top-deck (value 5) and 3 beads from the bottom-deck (each with a value of 1, totaling 3); the sum of the column (5+3) is 8.
Similarily, the fourth column representing the number 7, is composed of 1 bead from the top-deck (value 5) and 2 beads from the bottom-deck (each with a value of 1, totaling 2); the sum of the column (5+2) is 7.
Evolution
On each rod, the classic Chinese abacus has 2 beads on the upper deck and 5 on the lower deck; such an abacus is also referred to as a 2/5 abacus.
The 2/5 style survived unchanged until about 1850 at which time the 1/5 (one bead on the top deck and five beads on the bottom deck) abacus appeared. It lasted until around 1930 at which time, the 1/4 abacus, the present day style preferred and manufactured in Japan, appeared. The 1/5 models are rare today and 2/5 models are rare outside of China (excepting Chinese communities in North America and elsewhere).
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.
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 all of the fingering technique is obfuscated by the mouse. With a real abacus, constant practice is indispensable in achieving virtuosity and calculating speed.
The Abacus Today
The abacus is still in use today by shopkeepers in Asia and "Chinatowns" in North America. (The photograph on the right, dated September 1997, taken in Beijing, China, by Peter Wouda, shows a store clerk using the abacus.) Its use is also taught in certain schools in Japan and in the U.S. In fact, it is used to teach mathematics to blind children in situations where a sighted person would use pencil and paper. The enduring interest in this ancient device is also demonstrated by the more than 200 hits this page receives daily, from around the world.
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