Trapezoid! I choose you!

Okay, let's get the math out of the way first.

Polygons: A closed shape, consisting of straight lines that don't overlap each other. They can be *concave* or *convex*. **Regular polygons** have all sides congruent, and all angles congruent. Thus, regular polygons must be convex, with interior angles less than 180 degrees.

You might want to avoid this Definition: Polygon. Or you might want to read the comments for your own amusement.

As mentioned in the comic above, if you draw all the diagonals from one point, you divide the polygon into triangles, each with 180 degrees, and the sum of those is the sum of the interior angles. There will always be two fewer triangles than there are sides, which is the source of the *n less two* line in the song. Note that a triangle has no diagonals and is composed of a single triangle of 180 degrees, the trivial case for this rule.

About the comic:

In case anyone reading this is new to this blog or my webcomic *(did you come from a #PokemonGO or #TMC16 hashtag?)*, I did want to explain a little about the characters above. They are NOT supposed to be the characters from the show. They are semi-occurring characters made up to imitate the characters in the show ... a little ... sort of. Except for Melissa (aka Missy), she's new. I won't comment on Mr. Wayne's anime-styled hairdo.

The two in the bottom panel, as regular readers know, are math teachers who regularly appear in the strip, but it's summer break, so they're in the yard, having just been in the pool.

For the long-time readers who think they missed something: Judy is the other English teacher who is sometimes seen with Michele. Her boyfriend is Chuck, who appeared a few times in the early years. He works in an office with Frank, aka "Uncle Frank", who has actually appeared more often -- generally, any time I need someone old and tired to express something. Frank, a leap baby, was introduced as being 40, but he's apparently a bit older.

One of these days, I have to do a character map, or at least update a wiki page somewhere.

As for the **Polygons** in the picture: only two are supposed to be something. The beaked one on the bottom came from
comic #957.

I wanted to include a Pentagon with an army theme, but I've done that before. (In actuality, it just wasn't going to fit. You understand, right?)

Finally, I was going to have one of the kids catch a Polygon in a Polyball, and show the figure (the above-mentioned Pentagon) *inscribed* inside the circle. But I couldn't fit "inscribe" or "circumscribe" in the song! There aren't a lot of good rhymes.

While I'm at it, there aren't a whole lot of useful rhymes for *shape* either!

Forgive the long missive. I'm not usually this wordy. If you're new here, click on the "Comic" tag to see more. Or just explore. Thanks for stopping by.

*Come back often for more funny math and geeky comics.*

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