This section is about the many numerical systems, since mesopotamia until the binary system.

We are accustomed to numbers. Everyday we pass by a number on the streets, we have to remember our documents number, our address and so on. But how natural is the process of **counting**.

In mathematics counting is the same thing as associating a set A to a set B through a function. For example, the set A might be your fingers and the set B a colection o objects.

The Mayas

The Mayas were a civilization that lived around the year 2000 b.C. in the Yucatan peninsula.

It comes naturally to us to count from 1 to 10 using our fingers. It seems that the Mayas decided to use their toes as well. It is not known for sure why they chose a base 20 system for their calculations, but perhaps it was because of the astronomy it required. We know that 20 is a multiple of 2, 5 and 10, maybe that’s why having three multiples is an advantage in any number system especially when a number has to divide angles of 360, 180, 90, 45 (inclined plane), 15, 5 degrees.

As we can see in the figure above, the Mayas used a circle for the unitary value (uinals) and the bar worth 5 uinals[1]. But what about zero?

References

[1] Salyers, Gary D. “The Number System of the Mayas.” *Mathematics Magazine*, vol. 28, no. 1, 1954, pp. 44–48. *JSTOR*, https://doi.org/10.2307/3029437. Accessed 25 Jan. 2023.

[2] BLUME, ANNA. “Maya Concepts of Zero.” *Proceedings of the American Philosophical Society*, vol. 155, no. 1, 2011, pp. 51–88. *JSTOR*, http://www.jstor.org/stable/23056849. Accessed 25 Jan. 2023.

Images

unknown Mayan (Mayan cultural designation). *Uxmal*. 8th-11th centuries. *JSTOR*, https://jstor.org/stable/community.3998630. Accessed 25 Jan. 2023.