The abacus is a mechanical aid used to perform arithmetic calculations (sometimes called bead arithmetic). It is believed that the counting board, ancestor of the abacus, first appeared around 3000 B.C. as an arrangement of sand and pebbles and was developed over the next 4,500 years into the modern abacus. Such devices evolved from the need to count things without having to remember what was counted. For example, merchants needed a way to count goods bought and sold and to preserve these figures. The abacus and kindred devices functioned efficiently in this capacity until paper and pencil became commonly available (and even after, in some parts of the world). The abacus is considered by many to be the ancestor of the calculating machine and the computer.
The evolution of the abacus is often divided into three periods: ancient times, Middle Ages, and modern times. The earliest counting boards, dating to the ancient Greek and Roman period, have not survived due to the ephemeral materials used in their construction; these earliest counting boards probably consisted of lines drawn in the sand and small pebbles placed within those lines. (The word abacus is probably derived from the Hebrew ibeq, "to wipe the dust," or abaq, "dust.") The oldest surviving counting board is the Salamis stone tablet, circa 300 B.C. In the Middle Ages, counting boards were made from wood, stone, or metal, and bore carved grooves or painted lines between which beads, pebbles, or metal discs were placed. The modern abacus (suan-pan, in Chinese) appeared around A.D. 1200 in China and was constructed of either stone or metal. Beginning in about A.D. 1600, the Chinese abacus was adopted and evolved by the Japanese, who called it soroban.
The modern abacus, as shown in Figure 1, is constructed of various hardwoods and comes in many sizes. The frame of the abacus possesses a series of vertical rods (or wires) along which a number of wooden beads can slide freely. A horizontal beam or crossbar separates the frame into two sections, often known as the upper deck and the lower deck. Each column represents one digit place in the decimal system; the column farthest to the right is the ones column, the next column is the tens column, and so on. The user performs calculations by manipulating the beads. When a bead is "counted off" as part of a calculation, it is moved from the origin (i.e., its position away from the beam, whether at the top of the upper deck or the bottom of the lower deck) into position against the beam. Each bead in the upper deck has a value of 5; each bead in the lower deck has a value of 1. 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 next column over on the lower deck (next-highest digit). Calculations involving numbers with a fractional part, such as 3.14, are performed by arbitrarily designating a space between two of the columns as the decimal point. All the columns to the right of this space then represent fractional portions while all the columns to the left represent whole number digits.
When calculating 7 + 2, one begins by moving 1 bead down from the upper deck to the beam (total value = 5) and 2 beads from the lower deck up to the beam (total value = 2), recording a 7. Next, one moves up 2 more beads from the lower deck (same column), thus adding 2 to 7. The sum is then read off from the resultant bead positions: 1 bead down from the upper deck (5) plus 4 beads up in the lower desk (4) equals 9. (In such a trivial case there is of course no gain from using the abacus, since adding 5 + 4 mentally is no easier than the original problem. However, for larger numbers the abacus becomes truly useful.) Subtraction is performed by first positioning beads to represent the minuend (number from which subtraction is to occur) and then removing the appropriate number of beads for the subtrahend (number which is to be subtracted). The final bead positions represent the answer. For instance, when calculating 9 - 7, one moves 1 bead down from the upper deck (5) and moves 4 beads up from the lower deck (4) to represent 9. To subtract 7 from 9, one moves 1 bead back up on the upper deck (-5) and 2 beads down on the lower deck (-2). The remaining 2 lower-deck beads against the beam represent the result (9 - 7 = 2). In order to perform multiplication and division, the abacus must be expanded to include additional decks.
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