A Poet Completes the Square

Sue VanHattum and I were chatting about her young adult math books.

[Sue would love to get your help with beta-reading her books. Scroll down to the bottom of this post for details.]

In the first book of the series, Althea and the Mystery of the Imaginary Numbers, Althea learns that Tartaglia came up with a formula to solve cubic equations and wrote about it in a poem.

Sue had discovered an English translation of that poem and shared it with me. (You can read it on JoAnne Growney’s blog.) Then we wondered whether we could come up with a simpler poem, something an algebra student might be able to follow.

Perhaps you and your kids would enjoy making up poems, too. An algebra proof-poem might be too difficult for now, but check out my blog for math poetry ideas.

How to Complete the Square

Has it been ages since you studied completing the square? I like the way James Tanton explains it in this video:

I began by remembering how, back when algebra first started, there weren’t any letters or symbols. The mathematician al-Khwarizmi described his reasoning with words, using squares and roots (the sides of the squares) for the unknown quantities.

Once I decided how to name the constants, my poem began to come together.

And here it is, with algebra equations scattered between the stanzas to help you follow the math.

Quadratic Formula

Exploring, I find some Amount of squares,

And look, a Bundle of roots lying there.

A Collection of extra pieces I brought.

Yet taken together, it all comes to naught.

The roots are the root of the problem, you see.

What value the root? Say, what can it be?

I’ll set the Collection for now to the side.

While I study the root, that Collection will bide.

Multiply the Amount clear across, if you please,

For squares upon squares will make factoring a breeze.

Now if only the Bundle could evenly share.

I’ll take it times four because that keeps the square.

Next add a square Bundle, to factor it right.

(On both sides, remember!) The end is in sight,

For now, I’ve assembled a beautiful square,

And see, the discriminant waits for me there.

Take the square root, and everything’s fine.

(But never forget that plus/minus sign!)

At last, solve for x, my root from the start.

The solution complete, for math is my art.

Will You Help with Sue’s Math Stories?

Sue is a retired community college math teacher who now teaches with Art of Problem Solving. She has also run math circles, edited Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers, and played with all sorts of math herself.

She’s writing a series of math stories for teen (and adult) readers.

Sue says…

I’m writing Althea’s Math Mysteries, a series of 4 young adult novels with math at the center. The first two books are done. My publisher, Natural Math, needs to get feedback from more young readers before publishing.

Request 1: Readers ready to give feedback

If you have a kid who enjoys both math and reading, who has the fundamentals of algebra down and would like to give feedback, I’d like to connect. (Anyone whose feedback helps me improve the book will be mentioned in the acknowledgements.)

Althea and the Mystery of the Imaginary Numbers has some history and some math. Althea and her mom are discussing complex numbers. In Althea and the Mysteries of Triangles, Circles, and Pi, three of Althea’s friends join her, and her mom leads them on some mathematical adventures.

(These are not ‘whodunit’ mysteries. The mysteries are in the math.)

If you and/or your child are interested, please let me know which book you or they would like to read. The books do not need to be read in order. Yes, you can read both.

Email me at: altheasmathmysteries@gmail.com

Request 2: Help with course design

I am designing a course to go with the second book. It’s a bit of geometry and a bit of trig, and does not cover all of either of those courses the way they are usually taught. I will not give grades, but I will engage with each student’s questions and comments.

Are you a parent of a child who might want to take this course? Would you like to help me design it? If so, contact me.

I will offer this course free the first time (hopefully in September). If it goes well, it will help me improve the book, and I might teach it again (but then it’s likely to cost).