Central American Number Systems
Maya and Aztec
Maya:
• The Maya civilization existed by 300 B.C.
• Millions of people still speak the Maya languages and preserve the Maya culture.
• Though the Maya fought fiercely for their independence, they were defeated by the guns
of the Spanish cavalry.
• All but 3 or 4 of the Maya books were burned by the invaders, however, the Maya
numerals survived.
• The Mayan numeral system is the earliest known system to use a zero placeholder.
• Instead of writing place values from right to left across the page as we do now, they
wrote in columns with units on the bottom.
• Only three symbols were needed to write any possible number: a dot, a bar, and a shell.
• Was “almost” a base-20 system.
Mayan number system:
In a standard base-20 system, the right-most digit is the 1’s place, the second digit is the _____
place, the third digit is the _____ place, the fourth digit it the _____ place, etc.
In the Maya system, the first digit is the 1’s place, the second digit is the _____ place, the third digit
is the _____ place, the fourth digit it the _____ place, etc.
Properties (or more strictly, “non-properties”) of the Mayan number system.
The Mayas appear not to have had fractions, but they were still able to make remarkably accurate
astronomical measurements. The Mayas almost certainly did not have methods of multiplication for
their numbers and definitely did not use division of numbers. Yet the Mayan number system is
certainly capable of being used for the operations of multiplication and division.
Since the Mayan numbers were not a true positional base-20 system, it fails to have the nice
mathematical properties that we expect of a positional system. For example,
Calculate (9, 8, 9, 13 ,0)M
Calculate (9, 8, 9, 13)M
Now find 20 × (9, 8, 9, 13)M
(9, 8, 9, 13 ,0)M = 0 + (13 × 20) + (9 × 18 × 20) +
(8 × 18 × 202 ) + (9 × 18 × 203 )
= 1,357,100
yet
(9, 8, 9, 13)M = 13 + (9 × 20) + (8 × 18 × 20) +
(9 × 18 × 202)
= 67,873.
Moving all the numbers one place to the left would multiply the number by 20 in a true base 20
positional system yet 20 × 67,873 = 1,357,460 which is not equal to 1,357,100. For when we
multiply (9, 8, 9, 13) by 20 we get 9 × 400 where in (9, 8, 9, 13, 0) we have 9 × 360.
Aztec:
•
The capital of the Aztec Empire was called Tenochtitlan, the site where Mexico City now
stands.
•
Pyramids and temples flanked the great plazas of the city. A sewer and water system
safeguarded health and sanitation. Great markets served the needs of 50,000 customers a
day.
•
In 1519, the Spanish army found the city amazing. There was nothing like it in Europe at
that time, with the size, splendor, or cleanliness.
•
The Spanish army invaded the city and took over. In doing so, they burned most of the
Aztec books, so our knowledge of their mathematics is limited.
•
The Aztec’s had a base-20 system. They had an additive system that they used for general
numbers.
•
They appear to have had a different numeral system for land records. This system was still
base-20 but was a positional system. This system also had a “zero. ”