Mayans used more than one numeric system on their stone monuments and scriptures, in which numbers were represented by combinations and variations of hieroglyphs for positions and values. The hieroglyphs looked like the heads of various gods, animals, or sacred objects. The symbols for 0, 1, and 5 look like a shell, a dot, and a line.
Mayans counted in base 20 (vigesimal system), but their two calenders were more complicated variations. The Tzolkin calendar consisted of 13 months of 20 days and was used mainly for religious purposes. The Haab calendar was used mainly for worldly affairs and astronomy; it had 360 ordinary days and five that were called the nameless days: Uayeh.
Dates were often represented by giving them in both calendars. However, these combinations repeated after 18,980 days (52 sun years or 73 religious years): .
Potential ambiguities were resolved by adding the number of days since an assumed birthday of one of their gods. In 1935 Eric S. Thompson found that date: August 3113 B.C.
This invariant calendar uses a vigesimal system except for the value in the second-lowest position of their numerals, which ranges between zero and seventeen. This notation omits the hieroglyphs for the positional values;only the values are shown. The third positional value in the resulting system is 360, which approximates one year.
The Thompson concordance: J. E. S. Thompson, "Maya Chronology: The Correlation Question," in Contributions to American Archaeology, 3(13-19), Carnegie Institution of Washington, 1937 pp. 51-104 and J. E. S. Thompson, Maya Hieroglyphic Writing: Introduction, Washington: Carnegie Institution, 1950.