The classical Mayan period of civilisation dated from 250900 AD, although their civilisation started well before this. Their civilisation collapsed in the 9th century AD, so this system is not used any more. The Mayans had an interesting number system with a base 5 within a base 20. Enter a number from 1 to 99999 to see how the Mayans would have written it, or enter a number to count with. 
The Mayan system is interesting as they developed it without any contact with the other systems on this website. It is similar to the Babylonians but the Mayans chose different numbers as their bases. They used dots to represent numbers under five, so four is four dots. Five is represented by a line. So six is a line and a dot, and seven is a line and two dots, and thirteen is two lines and three dots. This is a unary system, but using five as a base rather than the more common ten.
1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19 

This works up to nineteen, but rather than twenty being four lines, they started a new count above the first one. Zero is represented by a shell. So twenty is a single dot above a shell. This stacking of numbers rather than having them in a line is a little disconcerting at first! You have to talk about rows rather than columns. This second system, for counting the twenties and powers of twenty, is positional, and even has a zero, to show that you have no digit in this row.
20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40 

To calculate a Mayan number, you need to divide the number into powers of twenty.
5124 = 12 x 20 x 20 + 16 x 20 + 4 = 

The great advantage of the positional system is that you need only a limited number of symbols (the Mayans only had two, plus their symbol for zero) and you can represent any whole number, however big. The Mayans had a sophisticated number system, but a little complex. Presumably the Mayans chose five and twenty as the two bases of their system as there are five fingers on one hand, and twenty fingers and toes on one person. Although we think of other systems using base ten, in fact the Romans had almost a base five within their base ten, as they had separate symbols for five, fifty, and five hundred. An eastern abacus has beads for five as well as beads for units. It makes sense, as it is hard to instantly recognise groups of symbols more than five. Some peoples, like the Babylonians arranged them into neat patterns to make it easier, but then it became harder to draw. The Mayan system is quick to write, and simple to understand. However, multiplication tables need to be learned up to twenty, rather than just ten!
The Mayan had a second Number System, used for dating buildings and on Calendars, etc. This would be a more formal system, rather than a number system used for calculation. The following was sent to me by Zoe Anne (Hemphill) Tom, who drew it.
© Jo Edkins 2006  Return to Numbers index