Why do so many of my students use incorrect names for various polygons? They claim that they are merely recalling what they have been taught; maybe this is so, maybe not. I suppose there are two major possibilities:

- They are
*remembering*incorrectly. - They really were
*taught*incorrectly.

Since this is Weston, I would prefer to believe it’s #1…but I have to admit that it might be #2, even in Weston.

Of course we shouldn’t just throw around the claim that certain names are incorrect without producing an argument for what the *correct* names are. Some of my students want to look in Wikipedia or count Google hits, but those methods lead to popularity contests, not truths. As I said in an earlier post, you can usually trust Wikipedia for mathematical information, but names occupy a middle ground between math and English, so Wikipedia is less reliable in this case than with pure math. As a better starting point, here is Wolfram Mathworld’s reasonably authoritative list of names for polygons with *n *sides:

n |
polygon |

2 | digon |

3 | triangle (trigon) |

4 | quadrilateral (tetragon) |

5 | pentagon |

6 | hexagon |

7 | heptagon |

8 | octagon |

9 | nonagon (enneagon) |

10 | decagon |

11 | hendecagon (undecagon) |

12 | dodecagon |

13 | tridecagon (triskaidecagon) |

14 | tetradecagon (tetrakaidecagon) |

15 | pentadecagon (pentakaidecagon) |

16 | hexadecagon (hexakaidecagon) |

17 | heptadecagon (heptakaidecagon) |

18 | octadecagon (octakaidecagon) |

19 | enneadecagon (enneakaidecagon) |

20 | icosagon |

30 | triacontagon |

40 | tetracontagon |

50 | pentacontagon |

60 | hexacontagon |

70 | heptacontagon |

80 | octacontagon |

90 | enneacontagon |

100 | hectogon |

10000 | myriagon |

Let’s see what we can do with this list. I make the following observations:

- The very existence of a two-sided polygon sounds doubtful to most people. We’ll discuss this one below.
- Three- and four-sided polygons, being the most common ones, commonly have Latin names (
*triangle*and*quadrilateral*), even though there are also alternative Greek names, which are very rarely used. - All other polygons have Greek names. Therefore nobody ever calls a six-sided polygons
*sexagon*or*sextagon,*and nobody calls a seven-sided polygon*septagon,*no matter what my students claim. - For some mysterious reason, the 11-sided polygon is listed here not only as
*hendecagon*(the correct name, from the Greek*hendeca*, meaning*11*), but also with an incorrect alternative Latin-Greek name,*undecagon*. I see no reason to do this. In fact, another Wolfram Mathworld page makes this observation: - Somewhat similarly, but worse, the 9-sided polygon is listed in both the Greek form,
*enneagon,*and the hybrid,*nonagon*— but here Mathworld oddly prefers the Latin-Greek hybrid to the pure Greek. On their other page, however, they make this observation:

A hendecagon is an 11-sided polygon, also variously known as the undecagon or unidecagon. The term “hendecagon” is preferable to the other two since it uses the Greek prefix and suffix instead of mixing a Roman prefix and Greek suffix.

The nonagon, also known as an enneagon, is a 9-sided polygon. Although the term “enneagon” is perhaps preferable (since it uses the Greek prefix and suffix instead of the mixed Roman/Greek nonagon), the term “nonagon,” which is simpler to spell and pronounce, is used in this work.

Even though counting Google hits is a useless way to decide these issues, let’s check them out just for fun:

- 14,900 hits for “hendecagon”; 12,400 for “undecagon.” Hooray!
- 18,400 hits for “enneagon”; 69,500 for “nonagon.” Boo, hiss!

Oh — I also promised a discussion of two-sided polygons, didn’t I? Most people think they don’t exist, so they don’t need to be named. (Unicorns don’t exist, but they still have a name. Hmm….) Actually, however, they do exist: for example, start at the North Pole, draw a line segment along the prime meridian until it reaches the South Pole, and then draw another line segment from the North Pole along the 90° longitude line, also stopping at the South Pole. Voilà: a two-sided polygon! You may think I’ve cheated, since this polygon exists on the surface of a sphere, not on a plane, but it might be worth imagining that you lived on the surface of a sphere, not on a plane… Anyway, I’ve never heard the term *digon* before; I’ve seen *biangle* and *bigon,* however. Be sure to pronounce *bigon* with a long *i, *and think of the famous saying, “Let bigons be bigons.” Again we can check Google hits, useless though it may be: 14,600 hits for “digon,” 487 for “biangle,” and 7,330 for “bigon.” Even though “biangle” loses the popularity contest, I suspect that it’s the best choice, since it’s consistent with the general principle: **use Latin names for polygons with four sides or fewer, Greek names for those with more than four sides, and hybrid names for none**.

Categories: Linguistics, Math, Teaching & Learning, Weston