Examples

Each stage is multiplied by a power of 20, and the value of the lowest floor is multiplied by 20 ^ 0 (x1), the second floor with 20 ^ 1 (x20), the third floor with 20 ^ 2 (x400 ) and so on ...
Which gives:

Value Mayan numbers note 27 1 * 20 +7 358 17 * 20 +18 340 17 * 20 +0 112211 14 * 8000 +0 * 400 +10 * 20 +11

Three columns of glyphs from La Mojarra Stela. The left column uses Maya numeration, representing the date 8.5.16.9.7 in Long Count , or the year 156 AD.

The Maya system, an irregularity in the case of dates : the third floor does not count a 400-360-but a groin groin (20 18). This postponed the next stage, not to the groin 8000-7200-but in the groin (20 18 20) and fifth in the groin-144 000 (20 18 20 20).

Addition and subtraction

Add or subtract the result is less than 20 counts with Maya is very simple
The addition is performed by the combination of symbols at each level.

If the result is five or more points, five points are removed and replaced by a line. If the result is four lines or more, four features are removed and a point is added to the next level:

+ = (4 +12 = 16)

The method is similar to the subtraction : remove items from the second to the first symbol.

If there is not enough points in the first symbol, a line is replaced by five points. And if, at any given stage, there are not enough features, a point is removed from the top floor being replaced by four strokes at the working level of:

- = (27-10 = 17)

Cardinal Health's zero Maya

The codex form of zero is not a shell. This sign is an elongated blade (including a sacrificial knife) and probably derives from the sign of polished obsidian mirror. The shell form is rare but attested.

On the monuments, the Cardinal never zero this form, but of a half flower with four petals, or that of a head characterized by the hand of the performance, or even a flower or corn the mirror of obsidian.

Variants graphics

Maya scribes had, besides the point number system / bar above many graphic forms to represent the twenty digits needed to write their numbers (often times) or units of credit system time (the period glyphs: kin, uinal, tun, katun, baktun, etc..). The most famous is certainly the system cephalomorphic numbers (each number from 0 to 19, is represented by a glyph in the shape of a head).

Two zeros Maya

Maya scribes used a vigesimal count (based on twenty) and they had in hand the two zeros distinct, marked by different glyphs. In general, they always carefully distinguished the times (such as 'cardinal') and dates ( nature 'ordinal'), for example in divinatory almanacs, writing the first black and second in red. Similarly, they carefully distinguished figure of the constituents (eg, two points '..' juxtaposed horizontally to form the number or the number 2) and the number of components (that is to say the digits of a number in positional writing, for example, two points': 'juxtaposed vertically to form the number 21 or a twenty-one').

The first, which can be called zero cardinal is a zero position, like the decimal numeration or any other position. For example: 9.9.16.0.0. (Dresden Codex p. 24) notes the term 9 - baktun 9 - katun 16 - TUN 0 - 0 uinal - kin, that is to say the duration of 9 x 400 tun (account year of 360 days) + 9 + 16 x 20 tun tun + 0 uinal (month 20 days) + 0 kin (day).

The second ordinal or zero was used to record the first day of the 18 months of twenty days or the additional period of five days that constitute the solar year (the ha'ab of 365 days). For example, the first of the year was 0 Pop.

The ordinal zero is evidence for the first time by a jade pendant (known as the Leyden plate ), and dated 17/09/320 (AD). In this pendant, the same glyph also appears in a "literary" in which he notes the verb denoting the action of the throne, the coronation of the king, whose face appears on the front of the plate.

The Cardinal is zero for the first time on 18 and 19 of steles Uaxactun, with three occurrences of this sign in the final position. They are found in the expression (redundant, since, in this double example, all units are expressed) to a date long count (that is to say, represented by the time expressed in number of days since the origin of the Mayan chronology, or 3113 BC): 8 - baktun 16 - katun 0 - 0 tun - uinal 0 - kin. Zero cardinal Maya is attested since February 2 357.

Count Spoken (Yucatec, data Beltran, XVIII ^century)

Top of the list of names of numbers Yucatec extract: Beltran de Santa Rosa Maria, Pedro (1742): Arte del idioma Maya reducido a sucinta reglas y semilexicon yucateco.

Suggestion. The component you (tuy front vowel) is the contraction of rental ti 'verse,' and the index of ^3-person staff-u 'sound', which is used to derive the ordinal from cardinal (as our suffix which is from 3 to ³ rd). The rental can be understood, then the index remains staff (eg. In 50). The confusion over, ti + u, can also be implied. For example, expression 35 given by Beltran is a shortened form of holhu you-ca-KAL which recognizes holhu the numeral '15 '(actually the compound system (5,10)), the term sub- you heard the numeral prefix AC-'2 '(either to the ² nd) and the classifier able KAL' twenty twenty '. The shape holhucakal amounted ho.lahun ti + u-ca-KAL and translates element element: '15 to ^2nd TWENTY '.

These forms reveal the specific counts of pre-Columbian Mayan spoken, namely that the Maya had an operation we do not know our arithmetic. An operation that gives the result 35 when it is made to cover the arguments 15 and 40 (AC-KAL is also the name of forty). The linguist Claude Hagege proposed to call this operation "Operation protraction.

Andrew Cauty (1987) showed that the numeration Yucatec is a special type that can mean the ordinal type of prior retrograde vision. Indeed, if the expression of 35 says something like '15 to ^2nd TWENTY 'or '15 to 40', its numerical value 35 may not be obtained by returning the first period. Note that in the compounds of the twenty second (21 to 39), Yucatec does not usually specify the "coefficient" of TWENTY mentioned (and which can only be the "first", ie ie 2) as in the phrase you hun KAL 21, but not in 30 or 35 (which is the relator is that you implied).

References

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