Pre-Columbian numeral systems | Tangente

The Aztecs: an additive base-20 system -------------------------------------------

Around 1200, the Aztecs used an additive numeral system, like Roman numerals, but based on 20 rather than 10. In such a system, the symbols are added together to give the number represented. The Aztecs had four symbols: one for units, another for twenties, and the other two for 400 (20² = 20 × 20) and 8,000 (20³ = 20 × 20 × 20).

Thus, to represent the number 1,637, the Aztecs wrote four groups of 400, one group of 20 and seventeen units (since 1,637 = 4 × 400 + 20 + 17). The units were arranged in groups of five to make them easy to read. This system can represent numbers up to 19 × 20³ + 19 × 20² + 19 × 20 + 19, which equals 20⁴ – 1, or 159,999. To go any further, they would have needed an additional symbol for 160,000.