Counting Rod Numerals

Counting rods are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient China, Japan, Korea, and Vietnam. They are placed either horizontally or vertically to represent any integer or rational number.They are a true positional numeral system with digits for 1–9 and a blank for 0, from the Warring states period (around 475 BCE) to the 16th century.

Apparently, counting bars were used in China from the earliest times, but got forbidden later. As for Japan, the use of counting rod numerals continued to grow, and they had even become the symbol of algebra there.

Initially counting rods could be used for simple calculations, expressing digits from 1 to 9. However, later on their development led to the introduction of «zero» and a whole symbolical language of mathematics.

Counting sticks and a counting board helped a lot in complex calculations with fractions, fractals and negative numbers. To reflect the latter, either sticks of a different color or special forms of writing were used. Counting numeral rods are still used today in some parts of east Asia, predominantly China.