# The history of Mayan numbers

May. 04, 2009

## Who were the Mayas

The Mayas lived more than 20 centuries in the peninsula of Yucatán, in Mexico, Central America. In the beginning they lived in small groups, that cultivated: corn, beans and pumpkin, and had periods of great accomplishments. The decadence of this civilization had its beginning when the invasion of foreign people started, at the same time, the farmers were against the priests. It’s reported that the Maya civilization had been exterminated when conquered by the Spaniards.

May. 02, 2009

## Mayan Civilization

 Map of the Mayan area Ruins of Mayan city
May. 04, 2009

## The history of Mayan numbers

The Mayan numbering system used the following symbols: dot, bar and a shell, and this last one represented the zero, a concept used by the primitive Hindu civilization. The Mayas established the relative value of the digits in agreement with its position. Their system was based on the 20, so they could write with points and bars until the number 19, comas due to following rules:

1) The numbers from 1 to 4 are formed by a combination of points, for the number 1 one point was used, for the number 2 two points, for the number 3 three points, that were placed one beside the other.

2) The number 5 is represented by a bar, being placed one upon the other. Starting from those combinations points and bars are used.

Just like the Mesopotamian numbering system and ours, the Mayan was also positional, but the base is 20. For such a system, it is expected that the figures multiply powers of 20, which are 1, 20, 400, 8000 ..., but the Mayan system operated with an irregularity in this pattern: the position of 20 square, where the number should be multiplied by 400, it was multiplied by 360.Em result of this anomaly, the Mayan system, which had everything to be as operational as we, as positional and have a symbol to represent zero, was deprived of that benefit.

Just like the Mesopotamian numbering system and ours, the Mayan was also positional, but the base is 20. For such a system, it is expected that each digit multiply powers of 20, which are 1, 20, 400, 8000 ..., but the Mayan system operated with an irregularity in this pattern: the position of 20², when the number should be multiplied by 400, it was multiplied by 360. As result of this anomaly, the Mayan system (which would be as operational as our system, since it is positional, and had a symbol to represent zero), was deprived of that benefit.

May. 04, 2009

## Examples

Let’s transform the number 175 in a Mayan number step by step

Divide 175 per 20
175 ÷ 20 = you’ll get 8 times 20 and 15 units

20¹ : 8 x 20
•••
___

20º : 15 x 1
____
____
____

8 x 20 + 15 x 1 = 175

Now to transform a Mayan number in a decimal number we make the following:
we multiply each position per 20 and put it in the potency (n-

1), where n is the position where we are working on. The bases 20ºe 20¹ are set to facilitate the calculation:

20² : 3 x 360 =1080

•••

20¹: 5 x 20¹ = 5 x 20 =100
___

20º :8 x 20º = 8 x 1 = 8
...
___

1080+100+8=1188

The sum of the multiplication of each position makes 1188.

The Mayas used the four fundamental operations: addition, subtraction, multiplication and division, that calculation was made on the ground or even surfaces, to write they used stones and branches. It’s believed that to accomplish those operations they did a table where the points and bars were placed.

May. 03, 2009

## Examples of calculation based on number 20

Examples how to represent the 20

20¹ (.) 1x20
+ =25
20º (-) 5x1

20¹ (.) 1x20
+ =20
20º ( ) 0x1

20¹ (..) 2x20
+ =40
20º ( ) 0x1

The number 20 was very important for the Mayan, as well as the 4 and the 5: the 5 (five) was important because it formed an unit. And the 4 (four) because it forms 4 units of 5 that makes a person, and a person has 20 (twenty) fingers forming 5 x 4 = 20.

May. 04, 2009

## Mayan numbers - 1 to 19

File Type: MS Word Document: 21 K

May. 04, 2009

May. 04, 2009

## Addition in Mayan system

File Type: MS Word Document: 34 K

May. 04, 2009

## Subtraction in Mayan system

File Type: MS Word Document: 40 K