# Names of polygons

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:

1. They are remembering incorrectly.
2. 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:
• 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.

• 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:
• 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