Soroban in Various Number Systems

The Japanese Soroban is a counting device that is still widely used in the present day Japan. In all likelihood it was borrowed from China in the 16^th century. It is divided into two regions, of which the upper one is called the "heaven" and the lower the "earth". Unlike in the Chinese suan pan, each wire in the upper region of the soroban contains a single bead, that, when it is next to the (region) divider, represents 5. Originally, the wires in the lower region each contained 5 beads, but the redundant fifth bead has been dropped about 1920.

The number of beads, therefore, on each wire of the authentic soroban is 5 which is exactly half of the base (10) of the decimal system. This observations allows to expand the device to any positional system with an even base. The applet below implements that idea.

References

1. M. Gardner, Mathematical Circus, Vintage Books, NY, 1981

Copyright © 1996-2009 Alexander Bogomolny