The Mayans Mathematics

     The Mayans were the first civilization to have and use the concept of zero. They did not yet have a system to identify fractions or negative numbers, they only had whole numbers and zero. The number system they created was vigesimal which is based on multiples of 20. Unlike the multiple symbols we use for various numbers the Mayans had just three symbols to write any possible number. They had the dot which had a value of 1. The bar had a value of 5, and the Shell had a value of 0. These numbers are all written vertically in columns. The lowest position in a column was reserved for the numbers 1-19. After that, the next highest position in a column is used for multiples of 20. The next highest position in the column is used for multiples of 400 (20x20).

     Here is a couple examples of how to write some numbers. When writing vertically the vigesimal positioning system, to write 20 a zero is placed in the first position (base) with a dot on top of it, in the second position. The dot in this place means one unit of the second order, which equals to 20. To write 21, the zero would change to a dot (1 unit) and for the subsequent numbers the original 19 number count will follow in the first position. As they in turn reach 19 again another unit (dot) is added to the second position. Any number higher than 19 unites in the second position is written using units of the third position. A unit of the third position is worth 400 (20x20), so to write 401 a dot goes in the first position, a zero in the second and a dot in the third. Positions higher than the third also grow multiplied by twenties from the previous ones.