Monday Morning Math: The Method of the Cups

Let’s do some multiplication today! This method, called the the Method of the Cups because it creates a figure that looks like a goblet, was published in 1556 in the 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. (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.  Titles were longer back then).  This is what 875×978 looks like:

Here’s how it works: instead of multiplying the units first (5 and 8) it starts with the largest digits.  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.

Next is 7×9=63 of 70×900 which is put underneath the 56.  It continues in this way up until the end, and then each column is added to give the sum at the bottom, forming the base of the cup! (I’m not sure if that makes sense to just read about – it might make more sense to do yourself and then compare.)

Happy multiplying!

This method was published in comes from the article “Spanish Colonial Mathematics: A Window on the Past” by Ed Sandifer, which was published in the College Math Journal in September 2002 and first appeared in the blog in this post.

Monday Morning Math: Celebrating Notable Latinx/Hispanic mathematicians!

Good morning! Hispanic Heritage Month started on September 15, and each day this month the website Lathisms.org features a Latinx/Hispanic mathematician of note!  For example, so far this year:

September 15 featured Dr. Antonio Estevan Martínez IV.  He is a professor at California State University, Long Beach, and conducts research in Mathematics Education.

September 16 featured Dr. Greisy Winicki Landman.  She is a professor at California State Polytechnic University in Pomona and works with math majors at teachers (at all levels) throughout California.

September 17 featured Rafael Ceja Ayala, a PhD student at Purdue University. He is an applied mathematician and is looking at applications such as medical imaging and engineering.

These are just a few of the people featured on the sight, and you can enjoy a full month of new honorees!

Monday Morning Math: Flipping burgers

Good morning!  It’s a new school year here and time to start Monday Morning Mathing. =)   In the spirit of “It’s still summer, right?” we’ll talk about mathematics applied to grilling.  Specifically, can we use math to figure out whether or not burgers on a grill should be flipped only once, as some believe, or more than once?  And if more, how much more?  Jean-Luc Thiffeault, a mathematician at the University of Wisconsin in Madison, explored just this question. 

The mathematics involved used Heat Equations and Newton’s Law of Cooling, and assumes that  your burger is made of meat and that it’s cooked when it reaches 70°C (approx. 160°F). There is a lot of neat mathematics, including eigenfunctions, but the end result is that the math says that your burger will cook about 30% faster if you flip it more than once.  Interestingly, this matches the empirical evidence.  

If flipping twice is better, or at least faster, than flipping once, then is flipping thrice even better than that?  Well, a little bit, but it doesn’t make as much of a difference, and more than that really doesn’t matter.  So go ahead, flip your food a couple times on the grill, and enjoy!

I read about this in the department newsletter from Madison, but then looking online found this powerpoint, where I got the information.