Flippin’ Wizardry

Because I’m a math teacher, my services as demystifier of mathematical phenomena are sometimes requested by family and friends who find themselves sufficiently mystified by something mathematical.  Recently I’ve had a few people send me the link to the YouTube video, “How do japanese multiply??” [sic]

Based on some of the comments (e.g., “What the [flip] is this wizardry?”), there are at least a few people in the world who might like an explanation.  Here’s the original video, followed by my narrated solution, plus, for the nerdily inclined, a bonus example in base 6!  Can you imagine anything more fun?

Actually, if you want a much more interesting multiplication algorithm, take a look at Russian Peasant Multiplication.  Now that’s some [binary] wizardry.

…and the response…



Something deeply unsettling is afoot in the land of math education when I’m teaching the same backwards thing in the same backwards way it was presented to me as a high school kid.  To wit, combinations.

Here is the current state of the art, according to the big boys of Advanced Algebra publishing:

Fundamental Counting Principle ====> Permutations ====> Combinations ====> Pascal’s Triangle ====> Binomial Theorem  ====> Celebration

I submit that, when we do it this way, we’re double-charging our students for their attention.  We bog them down in unnecessary algebraic trifling, and we go out of our way to delay the payoff for just as long as possible.  It’s bad marketing, and it’s bad teaching.  And we don’t exactly get away scot-free in all this.  I know I’m in for a rough couple of weeks any time I have to close my opening lesson with, “Trust me.”

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It’s going to be a bit of a strange year for Friday the 13ths.  First of all, there will be three of them.  Now that’s not especially weird–it happens every few years–but it’s the first time since 1984 that they’ll be spaced precisely 13 weeks apart.  It’s also the last time until 2040 that we’ll have three of them in a leap year.  I got all this information from a story on the USA Today website, which featured some words from one Dr. Tom Fernsler of the University of Delaware, a math professor (naturally) who’s earned himself the nickname of “Dr. 13.”  An interesting tidbit from the good doctor, and bad news for the phobic: the 13th of the month is actually more likely to occur on a Friday than any other day of the week–688 times in a 400-year period.

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Check, One, Two

Myself and (then) SSgt Clark doing some math in Fallujah, Iraq

I used to be an artillery officer in the Marine Corps, and it’s sometimes fun to bring mathematical details of my former life into the classroom.  Not only is there some useful and interesting math to be found there, but it also buys me the occasional attention of the Call of Duty crowd.  Here is a simple application of Bayes’ Theorem to artillery safety.


Thanks to the book Group Theory in the Bedroom, by Brian Hayes, I finally found someone to blame for my geometry students’ daily growing hatred of mathematical language.  His name is Robert Recorde.  For those of you who, like pre-this-week me, have never heard of Robert Recorde, don’t worry: you’ve seen his handiwork.  Recorde was a 16th-century Welsh doctor, mathematician, and author of Whetstone of Witte (1557), the book in which the modern equals sign first appears.

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What’s in a Stuf?

First, New Year’s Resolution = more blog posts.  In that spirit…

A few days ago, teacher of math teachers and all-around math dude Christopher Danielson posted an interesting argument with the conclusion that Double Stuf Oreos are not, in fact, stuffed double.  I’ll summarize it here.

Using the nutritional info on the packages, you can easily verify that one serving of originals (3 cookies) is 160 calories, and one serving of the Double Stuf variety (2 cookies) is 140 calories.  If we let w be the number of calories in a wafer, and f be the number of calories in one stuf’s worth of “creme” filling, you can set up the following system of equations:

\begin{cases} 6w + 3f =160 \\ 4w+4f=140 \end{cases}

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