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Here is my picture of mathematics now. It is a ball of wool, a tangled hank where all mathematics react upon another in an almost unpredictable way. And then in this ball of wool, there are a certain number of threads coming out in all directions and not connecting with anything else. ... [T]he Bourbaki method is very simple: we cut the threads.

Amer. Math. Monthly 77 (1970)

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# Maya Cycles of Time

## Maya Number System

The Maya left evidence of a highly developed understanding of arithmetic, calendars, and astronomy, which was certainly as sophisticated as contemporary civilizations elsewhere in the world. By the end of the Late Pre-Classic Maya time period (400 BCE – 100 CE), they were using a positional number system which employed only three symbols: a figure resembling a cowry shell representing 0, a dot for 1, and a horizontal bar for five. The number 0 appeared as:

and the numbers 1 to 19 inclusive appeared as:

Numbers larger than 19 were written vertically, employing a vigesimal (base 20) system. For example, the numbers 43, 354, and 220 were written as follows.

The concept of a zero placeholder first occurred among the Olmec, the mother of all Mesoamerican civilizations. By contrast, an ancient Middle Eastern civilization, the Babylonians employed two symbols in a sexagesimal (base 60) system. Without a zero placeholder, though, they did not have the means to make a distinction, the way we do, between numbers such as 6 and 60 (or, in their case, 6 and 6 x 60 = 360). They used, instead, the relative size and spacing of symbols as well as the context to deal with such ambiguities.

The Maya used a modified or quasi-vigesimal number system, in which the value of the third place was 360 instead of 400, for calendric purposes.

Some authors claim that the Maya employed a pure vigesimal system for non-calendric purposes; however, all extant evidence of large numbers relates to the calendar.

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Monteferrante, Sandra, "Maya Cycles of Time," Loci (June 2012), DOI: 10.4169/loci003886