Goodbye hexagon, hello 6-gon!

October 10, 2015

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.

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