For all of you in the ol' US of A still trying to get your taxes filed, here's some news you can sympathize with.

Aztec Math Decoded, Reveals Woes of Ancient Tax Time
http://news.nationalgeographic.com/news/2008/04/080403-aztec-math.html


The original scientific article will be published in print in tomorrow's Science Magazine (http://www.sciencemag.org/), but it's already electronically published on their website. Turns out that this discovery was found in the codices Vergara and Santa María de Asunción, which have been seeing a lot of interest lately. These documents detailed the land tax for each family in the Tepetlaoztoc area, which ethnically was Acolhua, a "sister" culture to the Mexica (aka the "Aztecs" as we call them). 

What makes these Acolhua codices really stand out is that fact that they use phonetic symbols to record the family's names instead of pictograms more prevalent in other Aztec documents. Also, a positional number system was employed instead of the usual Aztec number system (see http://www.ancientscripts.com/aztec.html).

Now, in addition to these achievements, the new discovery reveals that ancient Acolhua mathematicians employed as many as five different equations depending on the shape of the plots. As both the length of all sides were recorded as well as the computed land area, it is possible to reconstruct which equations were used. In the simplest case where the plot is perfectly rectangular, multiplication of adjacent sides yields the land area. As the plot gets more complicated, other equations were used. The most complex method was to divide up an irregularly shaped plot along the diagonal, compute the areas of the two resulting triangles, and add the two areas back up. 

In addition, scientists also found special symbols for fractions: the arrow for 1/2, the heart for 2/5, and the hand 3/5, the bone for 1/5, and the arm for 1/3.  These were also used in the calculations in addition to whole numbers to calculate the total plot area. 

Central Mexico has always been seen as less scientifically advanced as the Mayas, but at least among the Acolhua people, it seems that they were just as accomplished.  This really shouldn't come as a surprise.  The most important Acolhua city, Texcoco, produced the poet/philosopher/engineer king Nezahualcoyotl, who in turn nurtured learning in his city by establishing schools of learning and created the greatest library in Mesoamerica (which unfortunately did not survive the Spanish conquest).  It's great that these codices are finally yielding their secrets and telling us the amazing achievements of the ancient people of Mexico. 

References:
[1] Williams, Barbara J, Jorge y Jorge, María del Carmen, "Aztec Arithmetic Revisited: Land-Area Algorithms and Acolhua Congruence Arithmetic", Science, Vol 320, 2008, pg 72-77.
[2] Harvey, H. R., Williams, B. J., "Aztec Arithmetic: Positional Notation and Area Calculation", Science, Vol 210, 1980, pg 499-505.