When I was little, my dad bought the 33 1/3 – rpm album for a musical, an opera or a ballet before we saw it.  We listened to that record for weeks, months even, before the show.  Now I do the same with my children except I download the album to my phone and we bluetooth it in the house / car.  Full disclosure: We haven’t taken them to an opera.

So, when we saw Hamilton, we knew all the characters, the music, and the lyrics.  We knew the ebb and flow of the plot, and not only that, we learned and re-learned so much American history by listening to the soundtrack.  But I started noticing more than that.  I realized that composer Lin-Manuel Miranda used the number 3 throughout his masterpiece.  The most obvious threes are the King George appearances and the duels.  This revelation made me think about the number three as an artistic device.

Creative types have been using 3 for centuries.  Jazzman Bob Dorough penned and recorded the song “3 is a Magic Number” for Schoolhouse Rock! in 1973.  3 really IS a magic number.

Artists such as da Vinci and Michelangelo used the 3-sided triangle in their compositions.

The Mona Lisa, Leonardo da Vinci 1503

Screenshot from Wikipedia

Notice how in the above painting there are two triangles – the triangle their bodies make with vertex up and the inverted triangle (vertex down) their heads form.  In addition, there are three people: Jesus, Mary and Joseph.  Of course Christianity employs the number 3 in a variety of incarnations, most notably the Holy Trinity: father, son, and holt spirit.

Authors use the number three as well in that there are often 2 male roles and 1 female role.  Think Harry Potter, Ron Weasley, and Hermione Granger, or perhaps Luke Skywalker, Han Solo, and Princess Leia.  The story narrative itself has three parts:  set-up, conflict, and resolution.

In a few days we will have to remember to write 2019 instead of 2018.  (It will be March before this is automatic for me.) The number 2019 is divisible by three. How do I know?  Because the sum of the digits 2 + 0 + 1 + 9 = 12 is a multiple of 3.  To me, this is really the magic of the number 3.  I can look at any number and quickly determine whether or not it is divisible by three.  Many numbers that appear prime (51, e.g.) are actually divisible by 3.  In a few more days, school will restart and in Algebra I we will be factoring polynomials.  Recalling divisibility rules will be paramount in our students’ success with factoring.  We learn divisibility rules in the upper elementary grades to manipulate fractions but never really apply them until we factor polynomials.  Here are some of the rules that are easy to mentally calculate:

And now I really must finish writing college recommendation letters for a handful of AP Calculus students.

Happy New Year 2017