TO LEARN MATHEMATICS: MAYAN MATHEMATICS IN BASE 10

It is currently accepted that, around 600 B. C. the Mayan civilization developed for the first time the mathematical abstraction of zero. To them zero, had a cosmic meaning also. They developed the zero six hundred years before the ancient cultures of India. The Mayan civilization is also known for its outstanding achievements in astronomy, architecture, medicine, and agriculture. Today it is considered one of the most important pre-Columbian cultures of America. They developed a vigesimal numerical system (base of 20) which has very advanced features, such as the positional system with zero as a place marker. They used only three symbols to construct a method for all the arithmetic operations. This system was so powerful that it enabled them to make predictions, with astonishing precision, of astronomical events and to calculate a calendar, which has a larger precision than the Gregorian calendar. They used a positional system of numeration similar to the one we use today. This means that each sign has a value depending on the position that it occupies in the representation of the number. The numbers are set in a vertical position to represent powers of twenty (running from bottom up). They used only dots, bars and zero to represent numbers. The Mayas represented the Zero as an empty seashell. There are large advantages in using dots, bars, and seashells to perform mathematical operations. The resulting method does not require tables of any kind, and it is powerful, dynamic, and ludic. It is an excellent tool for teaching since it gives intuitive knowledge of basic algorithms. In the following, we describe the Mayan system. We also describe the transformation to a numerical system of base 10. Then, we show the fundamental arithmetic operations to use as an educational proposal in mathematics.