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# Goodbye hexagon, hello 6-gon!

A colleague of mine once remarked how strange it is that while the Greeks talked about 6-cornered shapes and 4-sided shapes, we talk about hexagons and quadrilaterals. Why is it, aside from the historical accident that it is, that we persist in making people learn Greek to talk about shapes they see everyday?

And quadrilaterals and hexagons are the easy ones. What’s a 7-sided polygon called? It’s either a heptagon or a septagon—I never remember (do you?). What about a 12-sided polygon? That’s a dodecagon. Thirteen sided? No idea—no one ever taught me that one.

Our vernacular around polygons is tied to an ancient system of numeration that not even experts know. We’ve created a system where we can speak properly about only a select subset of polygons: triangle, quadrilateral, pentagon, hexagon, octagon. Those prefixes denote the numbers 3, 4, 5, 6, and 8. And while there are certainly some of you who know more, I don’t think we ever bother teaching more than this. It’s like teaching inches and feet, and not bothering with miles.

We couldn’t convert to metric in the US, but we can do something even easier when it comes to polygons: name them by number. Forget the name of the icosikaitetragon? Just call it a 24-gon. Heptagons and decagons are 7-gons and 10-gons. We could even call hexagons 6-gons.

The advantages are immediate and enormous. First, every polygon now has an easy, instantly recognizable name. We’ve removed the barrier of Greek between ourselves and shapes. Second, we’re reminded of the defining trait of the thing when we name it. It’s why we call it a red-breasted robin instead of a Turdus migratorius.

Do you agree? Before you answer, let me add one more point: mathematicians use this nomenclature already. We even say n-gon instead of polygon, just so we can decide what n is later, or use the variable in equations.

We could have gone further. The prefix -gon is just Greek for -angle, as in triangle (3-gon). And while 5-angle and 9-angle have a certain poetry, I like the staccato of 5-gon and 9-gon. And it’s not so bad to keep a little Greek in there.

Sure, it’s nice for students to know the word triangle. And you can argue that learning vocabulary for the polygons is fun. But do we really need to add barriers around mathematical objects when we could just call them what they’re called? Do kids need to know quadrilateral or heptagon to relate to 4-gons and 7-gons?? If you’re a math teacher, you can start calling pentagons 5-gons and decagons 10-gons tomorrow.

And the beauty of it is, your students will know exactly what you mean.

1. Gil Cerise

A great idea! Does this mean that a square is an equilateral 4-gon? Why not tackle the illogical naming of numbers while we are at it? That would also help kids learn math.

2. Simon Gregg

I liked this quote from Making Sense on Tracy Zager’s blog
https://tjzager.wordpress.com/2015/10/16/which-mistake-to-pursue/

“In traditional systems of instruction, teachers are asked to provide feedback on students’ responses, to tell them whether or not they are right…this is almost always unnecessary and usually inappropriate. Mathematics is a unique subject because…correctness is not a matter of opinion; it is build into the logic and structure of the subject…There is no need for the teacher to have the final word on correctness. The final word is provided by the logic of the subject and the students’ explanations and justifications that are built on this logic” (Hiebert et al. 1997, 40).

And I think we should make a feature of this logic, and the independence it gives learners. So I’m all for reducing the non-logical aspects that creep in, like Greek names. Let’s say it like the Greeks did, in our own language!

3. Roderick Kimball

I used to work at the National Museum of Mathematics I observed that kids and adults love identifying shapes by their Greek names. Knowing a special word for a five-sided shape that connects it with history is exciting. But simply labeling it according to its technical attributes? Not as much.

Everybody will want to draw the line in a different place, of course. I like calling an eight-sided shape an octagon, but if I want to refer to a 24-sided shape, I’m not going to call it an icosikaitetragon. But that’s just because nobody does. Nobody would know what I was talking about and the parts of that word don’t really associate it very well to anything else.

I believe there is great value in knowing these words we usually use and being familiar with the Greek prefixes. For example, learning that a shape with three sides is called a “triangle” is a child’s first contact with the idea that “tri” means 3 ANYWHERE WE SEE IT. The words learned through geometry help us to interpret the math embedded in everything else. Isn’t that what the study of math is for—to help us understand everything else? (aside from being great fun, of course)

To me, asking everybody to start saying “eight-gon” is somewhat like asking to say “eight-pus” and “three-cycle”.

Consider the task of a foreign language teacher. They teach their students a brand-new word for everything. I think it’s worth keeping a few words of mathematics around in order to preserve the connection between math, history and language.