Archive for May 5th, 2008

Cinco de Mayo Math

May 5, 2008

Today is the day many people (mostly in the US) celebrate Mexican Independence Day (nope that’s in September) the day in 1862 that the Mexican Army beat the French at Puebla, about 70-80 miles east of Mexico City. As part of this celebration, you might do some Cinco de Mayo Math by Paula J. Maida, which includes ideas like finding the proportion of colors on a Mexican Flag or writing the eleven letters CINCODEMAYO on wooden cacti and letting kids choose a letter randomly as a way to explore both probability and fractions.

Or, expanding beyond Mexico (as the celebration has in many places), you might read “Spanish Colonial Mathematics: A Window on the Past” by Ed Sandifer, which was published in the College Math Journal in September 2002 and is available as a .pdf file here from Ed’s homepage. As Ed explains in this interview:

[S]ome Latino students feel disconnected to math. But we can help make a connection by teaching about Spanish-colonial math and pointing to facts such as there were 11 math books published in Spanish in the New World before there were any in English, with the first being published in 1556, only 100 years after the printing press was invented.

The article above examines 7 of those math books. There’s the 1556 Sumario Compendioso de las quentas de plata y oro que in los reynos del Piru son necessarias a los mercadores: y todo genero de tratantes. Los algunas reglas tocantes al Arithmetica. Fecho por Juan Diez freyle. (Isn’t that a GREAT title!?! It translates as Compendious summary of the counting of silver and gold that are necessary in the kingdoms of Peru to merchants and all kinds of traders. The other rules touching on Arithmetic. Made by Juan Diez, friar.) which was full of all sorts of tables to help you out of you were a tax collector (Hey! More Tax Math!) and includes among other things the following example of how to multiply 875 by 978:

Isn’t this wild? Some of it is explained in the article: the initial 8×9 of 800×900 becomes the 72 of the upper left. Then 8×7 of 800×70 is 56, but this is written with the 5 below the 2 in 72 and the 6 next to the 72, making the 72 look like 726. Then 8×8 of 800×8 is 64, and the 6 of 64 is put next to the 5 while the 4 is next to the 726.

It continues in this fashion, with 7×9=63 of 70×900 put underneath the 56 and with all the numbers crammed together like Galley Division of the same time period. David Smith write in his book History of Mathematics (p. 119) that this method is essentially The Method of the Cup (per copa) because it looks like a goblet.

Several books followed the Sumario Compendioso…, including King Philip of Spain’s Pragmática sobre los diez días del año in 1584, which wasn’t so much about math as about how to deal with the fact that switching from the Julian to the Gregorian calendar involved skipping ten days, and several books that look at military mathematics and formations. In the latter category is the Breve aritmética por el mas sucinto modo, que hasta oy se ha visto. Trata en las quentas que se pueden ofrecer para formar campos y esquadrones by Benito Fernandez de Belo— another fabulous title which means Brief arithmetic for the most succinct method which has been seen up to today. Treating calculations that one can do for the formation of camps and squadrons — which shows how to align 278 men in a squadron into a regular pentagon and contains a woodcut doodle in the back. The final book in the article is the 1696 Cubus, et sphaera geometrice duplicata by Juan Ramón Coninkius about straightedge and compass constructons. Granted, the constructions (doubling the volume of a cube or sphere) were impossible, but that was still unknown at the time.

Happy Cinco de Mayo!