## 2300 Year old Chinese Calculator (Multiplication Table) in bamboo strips

5 years ago Tsinghua University in Beijing received a donation of nearly 2,500 bamboo strips.
They were muddy, smelly and are carbon-dated to around 305 BC when China was still not unified.
It must have been bought by someone illegally in Hong Kong market after being discovered during excavation of some ancient tombs.
Each strip was about 7 to 12 millimetres wide and up to half a metre long, and had a vertical line of ancient Chinese calligraphy painted on it in black ink.
These bamboo pieces constituted 65 ancient texts and are the most important artefacts from that period.

Strings that used to tie each manuscript together to form a scroll had long decayed. So the strips were all mixed up, few broken and others missing.
But, 21 bamboo strips stand out from the rest as they contain only numbers, written in the style of ancient Chinese.
These 21 strips turned out to be a multiplication table and when are arranged properly, a matrix structure emerges. The top row and the rightmost column contain, arranged from right to left and from top to bottom respectively, the same 19 numbers: 0.5; the integers from 1 to 9; and multiples of 10 from 10 to 90.

As in a modern multiplication table, the entries at the intersection of each row and column in the matrix provide the results of multiplying the corresponding numbers. The table can also help users to multiply any whole or half integer between 0.5 and 99.5. Numbers that are not directly represented, says Feng, first have to be converted into a series of additions. For instance, 22.5 × 35.5 can be broken up into (20 + 2 + 0.5) × (30 + 5 + 0.5). That gives 9 separate multiplications (20 × 30, 20 × 5, 20 × 0.5, 2 × 30, and so on), each of which can be read off the table. The final result can be obtained by adding up the answers.

This 2300 year old Chinese Calculator is effectively an Ancient Calculator of that generation.
This multiplication table must have been used to calculate agriculture and tax related informations like area of land cultivated, yield of crops and amount of taxes to be payed etc.
This Matrix can also be used to perform divisions and Square-roots.

The oldest previously known Chinese times tables, dating to the Qin Dynasty between 221 and 206 bc, were in the form of a series of short sentences such as “six eights beget forty-eight” and capable of only much simpler multiplications. The ancient Babylonians possessed multiplication tables some 4,000 years ago, but theirs were in a base-60, rather than base-10 (decimal), system. The earliest-known European multiplication table dates back to the Renaissance.

In later generation, Qin Shi Huang, China’s first emperor, united the country.
He subsequently ordered book burnings and banned private libraries in an attempt to reshape the country’s intellectual tradition.
Such ancient material were lost since then.