Unwinding "The Biggest Ball of Twine in Minnesota" Pt. 1

Weird Al's awesome song, "The Biggest Ball of Twine in Minnesota," prompted me to visit Darwin, MN when I was in the area. The ball is not just the biggest in Minnesota, but the world!  If we're talking sisal twine.  Made by one man.  (Turns out there are a lot of big twine balls).  The song always leaves me wondering whence the narrator originated. Here we'll unravel the lyrics and use math to help us understand.

Let's start at the beginning .

Well, I had two weeks of vacation time coming
After working all year down at Big Roy's Heating And Plumbing

Artistic license appears to have been taken, as all online references to this establishment on are related to the song's lyrics.  We can come back to this later.

Oh, we couldn't wait to get there
So we drove straight through for three whole days and nights

Maybe we can estimate an average speed, but how "straight" were they going?  Let's use some arbitrary paths to get an idea of the radius we should consider.

The Story of Maths

Here's a cool series to show in class if you can fit it in (or just to watch yourself).  The first two episodes are appropriate for a wide range of skill levels, visually engaging, and emphasize the multicultural history of math.  The next two give an overview of the development of math within the last 400 years or so, as the narrator visits sites of historical significance.  The Newton-Leibniz piece would be great to show at the outset of a calculus class, or when discussing the notation for derivatives.  The final disc explores prime numbers and the Riemann hypothesis, which holds special significance to the narrator, Marcus du Sautoy.

Fractal Magic Square

As I was watching The Story of Math with my class after finals, I thought I'd try a little experiment with the magic square shown in the video.



Each row, column, and diagonal sums to 15. Incidentally, if you add an amount n to each value, the square retains its magic and the sum changes to 15+3n.

But what if each unit square were comprised of nine smaller squares, like a sudoku board?  Could you follow the same overall pattern to generate a fractal magic square?

I made this one by adding successive multiples of nine to each mini-square, following the same "path" as in the original: