Considered one of the first mathematical instruments, the abacus has evolved significantly and so have the ways to use them. This Chinese Abacus also known as a Suan Pan has a 5+2 bead combination, with 5 earth beads and 2 heaven beads on a single rod split by a wooden barrier. The number of rods indicates the degree of accuracy of the calculated number for example 3 rods indicates a 3 digit number either 100, 010=10or 001 as 0.01. The choice of decimal point was dependent on the use.

The first description of Chinese abacus of this form was in a 190CE book of the Eastern Han Dynasty. The instrument was often used by merchants and shop keepers calculating costs.

The lower ‘deck’ of beads are commonly called earth or water beads and represent a value of 1 whilst the upper ‘deck’ are called heaven beads and represent a value of 5. The Chinese abacus had the 5+2 configuration as this also allowed hexadecimal calculations as Chinese weight units were hexadecimal [4]. This is done by having both heaven beads and all earth beads raised giving a value of 15 thus on a rod numbers between 0 and 15 can be displayed. Configurations of 4+1 can also be found and are often referred to as the Soroban (Japanese Abacus; ID: 213) however the two commonly interchange names.

The abacus was capable of multiplication, addition and subtraction and was very time efficient when used by a skilled person. Capable of doing a multiplication of 9 x 9 per rod this made it possible to multiply any numbers capable of fitting on the abacus together. Addition worked on the principle that you would add the appropriate value to each rod from right to left and carry any tens to the next row as needed, subtraction works very similarly but in reverse and might require ‘borrowing’ from more left rods. Multiplication was different and required individual mental multiplication of digit by digit left to right. For a 5+2 abacus two alternative techniques called the extra bead and suspended bead techniques could be used to make multiplication quicker [3]. These methods are still used today in some Chinese stores and Chinese abacuses can be found all around the globe. It is even thought that the Chinese abacus inspired the Roman abacus.

Japanese Abacus (Soroban): http://physicsmuseum.uq.edu.au/tomoe-soroban-abacus

*This item is part of the UQ Physics Museum Good Old days of Calculation Tour*

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