Maya numerals.
Maya numerals were a
vigesimal (
base-
twenty)
numeral system used by the
Pre-Columbian Maya civilization.
The numerals are made up of three symbols;
zero (shell shape),
one
(a dot) and
five (a bar). For example,
nineteen (19) is written as four dots in
a horizontal row above three horizontal lines stacked upon each
other.
Numbers above 19
Numbers after 19 were written vertically up in powers of twenty.
For example, thirty-three would be written as one dot above three
dots, which are in turn atop two lines. The first dot represents
"one twenty" or "1×20", which is added to three dots and two bars,
or thirteen. Therefore, (1×20) + 13 = 33. Upon reaching 20^2 or
400, another row is started. The number 429 would be written as one
dot above one dot above four dots and a bar, or (1×20^2) + (1×20^1)
+ 9 = 429. The powers of twenty are
numerals, just as the
Hindu-Arabic numeral system uses
powers of tens.
Other than the bar and dot notation, Maya numerals can be
illustrated by face type glyphs or pictures. The face glyph for a
number represents the deity associated with the number. These face
number glyphs were rarely used, and are mostly seen only on some of
the most elaborate monumental carving.
Addition and subtraction
Adding and subtracting numbers below 20 using Maya numerals is very
simple.
Addition is performed by combining the
numeric symbols at each level:
If five or more dots result from the combination, five dots are
removed and replaced by a bar. If four or more bars result, four
bars are removed and a dot is added to the next higher
column.
Similarly with
subtraction, remove the
elements of the
subtrahend symbol from
the
minuend symbol:
If there are not enough dots in a minuend position, a bar is
replaced by five dots. If there are not enough bars, a dot is
removed from the next higher minuend symbol in the column and four
bars are added to the minuend symbol being worked on.
Zero
The Maya/
Mesoamerican
Long Count calendar required the use of zero as a place-holder
within its vigesimal positional numeral system.
A shell glyph
--
-- was used as a zero symbol
for these Long Count dates, the earliest of which (on Stela 2 at
Chiapa de Corzo,
Chiapas
) has a date
of 36 BC.
However, since the eight earliest Long Count dates appear outside
the Maya homeland, it is assumed that the use of zero predated the
Maya, and was possibly the invention of the
Olmec. Indeed, many of the earliest Long Count dates
were found within the Olmec heartland. However, the Olmec
civilization had come to an end by the 4th century BC, several
centuries before the earliest known Long Count dates--which
suggests that zero was
not an Olmec discovery.
In the calendar
In the "Long Count" portion of the
Maya
calendar, a variation on the strictly vigesimal numbering is
used. The Long Count changes in the third
place value; it is not 20×20 = 400, as
would otherwise be expected, but 18×20, so that one dot over two
zeros signifies 360. This is supposed to be because 360 is roughly
the number of days in a
year. (Some hypothesize
that this was an early approximation to the number of days in the
solar year, although the Maya had a quite
accurate calculation of 365.2422 days for the solar year at least
since the early Classic era.) Subsequent place values return to
base-twenty.
In fact, every known example of large numbers uses this 'modified
vigesimal' system, with the third position representing multiples
of 18×20. It is reasonable to assume, but not proven by any
evidence, that the normal system in use was a pure base-20
system.
Notes
- http://www.museumofman.org/html/lessonplan_maya_math2.pdf
- No long count date actually using the number 0 has been found
before the 3rd century AD, but since the long count system would
make no sense without some placeholder, and since Mesoamerican
glyphs do not typically leave empty spaces, these earlier dates are
taken as indirect evidence that the concept of 0 already existed at
the time.
- Diehl (2004, p.186).
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