A mechanical counting device consisting of a frame holding a series of parallel rods on each of which beads are strung. Each bead represents a counting unit, and each rod a place value. The primary purpose of the abacus is not to perform actual computations, but to provide a quick means of storing numbers during a calculation. Abaci were used by the Japanese and Chinese, as well as the Romans.

REFERENCES:

Bogomolny, A. "Abacus in Various Number Systems." http://www.cut-the-knot.org/blue/Abacus.shtml.

Bogomolny, A. "Soroban in Various Number Systems." http://www.cut-the-knot.org/Curriculum/Arithmetic/Soroban.shtml.

Bogomolny, A. "Suan pan in Various Number Systems." http://www.cut-the-knot.org/Curriculum/Arithmetic/SuanPan.shtml.

Boyer, C. B. and Merzbach, U. C. "The Abacus and Decimal Fractions." A History of Mathematics, 2nd ed. New York: Wiley, pp. 199-201, 1991.

Fernandes, L. "The Abacus: The Art of Calculating with Beads." http://www.ee.ryerson.ca/~elf/abacus/.

Gardner, M. "The Abacus." Ch. 18 in Mathematical Circus: More Puzzles, Games, Paradoxes and Other Mathematical Entertainments from Scientific American. New York: Knopf, pp. 232-241, 1979.

Heffelfinger, T. and Flom, G. "The Bean Unbaffled--An Abacus Manual." http://webhome.idirect.com/~totton/abacus/.

Pappas, T. "The Abacus." In The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 209, 1989.

Pullan, J. M. The History of the Abacus. New York: Prager, 1968.

Smith, D. E. "Mechanical Aids to Calculation: The Abacus." Ch. 3 §1 in History of Mathematics, Vol. 2. New York: Dover, pp. 156-196, 1958.

Yoshino, Y. The Japanese Abacus Explained. New York: Dover, 1963.