The Mexica used a number system that combined elements of a vigesimal, or base-20, system with pictographic representations. The system used a series of signs for the numbers 1 to 19, and it combined these signs to represent larger numbers. The Mexica had a sign for 1, which was a dot or a small circle, and they had signs for 2 to 19, which were multiples of the dot. The Mexica also had a sign for 20, which was a flag-like symbol, and they had signs for 400 and 8000, which were the next orders of magnitude in the vigesimal system.
The Signs for 1-19
The Mexica number system used a series of signs for the numbers 1 to 19, and the signs were based on the dot, which represented the number 1. The sign for 2 was two dots, the sign for 3 was three dots, and the sign for 19 was 19 dots. The dots were typically arranged in a row, and the number was read from left to right. The Mexica also used a number of variants for the dots, including small circles, small lines, and small heart shapes.
The Mexica had a number of conventions for the arrangement of the dots, and the conventions varied by region and by period. In some cases, the dots were arranged in a single row, and in other cases, they were arranged in a more complex pattern. The Mexica also used a number of different signs for the same number, and the choice of sign depended on the context.
The Sign for 20
The Mexica had a special sign for 20, which was a flag-like symbol called pantli. The sign for 20 was used as a base for the higher numbers, and the Mexica would write a number of dots above the flag to indicate multiples of 20. For example, the sign for 40 would be two flags, and the sign for 60 would be three flags. The sign for 20 was an important element in the Mexica number system, and it was used in a wide range of contexts, from the calculation of the tribute to the recording of the calendar.
The sign for 20 was also used as a stand-alone symbol to represent the number 20, and it was used in a number of symbolic contexts. The Mexica believed that the number 20 had a special significance, and it was associated with the completion of a cycle and with the beginning of a new cycle.
The Signs for 400 and 8000
The Mexica had a sign for 400, which was a feather-like symbol called tzontli, and a sign for 8000, which was a bag-like symbol called xiquipilli. The signs for 400 and 8000 were the next two orders of magnitude in the vigesimal system, and they were used to represent very large numbers. The Mexica could combine these signs to represent even larger numbers, and they used them in a wide range of contexts.
The sign for 8000, the xiquipilli, was particularly important in the Mexica economy, since it was used to represent the number of cacao beans that were used in the major commercial transactions. The sign for 8000 was also used in the calculation of the tribute, and the tribute lists typically used the sign to represent the larger amounts.
The Use of Zero
The Mexica had a sophisticated understanding of the use of zero, and they represented it with a special sign — most commonly a stylized shell glyph, although flowers and other forms were also used. The Mexica use of zero, like that of the Maya, was one of the independent inventions of the concept in world history. The Mexica had a clear understanding of zero as both a number and a placeholder, and the use of zero allowed the Mexica to perform complex calculations, and it was an important part of their mathematical system.
The use of zero was particularly important in the calculation of the calendar, since the calendar required the use of zero to indicate the absence of a number. The Mexica were also skilled in the use of zero in the calculation of the tribute, and they used zero to indicate the absence of a payment.
Related Articles
- Mathematics and the Aztec Number System — the broader context
- How did the Aztecs use the vigesimal system? — the base-20 system
- What mathematical knowledge did the Aztecs have? — the broader knowledge
- The Tribute System and Imperial Wealth — the use in tribute
- The Aztec Calendar and Timekeeping — the use in astronomy
- Aztec Art, Architecture, and Science — the broader context