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# What Are Polygons?

What do a triangle, a rectangle, and a pentagon all have in common? They’re all polygons. What makes a polygon a polygon? And why do they matter? Keep on reading to find out!

By
Jason Marshall, PhD
Episode #221

## Simple and Complex Polygons

Objects in the polygonal zoo are further broken down into two additional types: simple and complex. In a simple polygon, no line segment ever cross over one of its buddy line segments that’s part of the same polygon. In a complex polygon, line segments can cross over each other as much as they’d like.

All regular polygons are simple polygons.

If you think about it, you’ll see that all regular polygons are simple polygons. In other words, they don’t intersect themselves and therefore have only a single boundary dividing their “insides” from their “outsides.”

A star-shaped polygon (with all of the criss-crossing line segments left intact) such as a pentagram is an example of a complex polygon. It still satisfies all the requirements to be in the polygonal club—namely it's a closed shape made from a bunch of straight lines in a plane—but it’s certainly not a simple one…literally.

## Polygons in the Real World

Now that your memory has been jogged and you remember that yes indeed you did once-upon-a-time learn what a polygon is, you might be wondering: So what? Why do polygons matter to you, me, and the rest of the world?

Let's start with the rest of the world—by which I mean nature. Because it turns out that polygons actually show up in the natural world.

Where might you see one in the wild? Well, there’s the hexagonal pattern of honeycombs, the somewhat mysterious hexagonally shaped storm on Saturn, the triangular or square or even more complex faces of naturally occurring crystals, and then there’s the truly bizarre and oh-so-remarkably hexagonal pillars of rock found at the Giant’s Causeway in Northern Ireland and Devil’s Postpile in California.

For me, the fact that polygons show up in nature, combined with the fact that they have tons and tons of fascinating mathematical properties (which we haven’t even begun to scratch the surface of), is more than enough reason to declare that in our world they definitely matter. Don’t you think?

## Wrap Up

OK, that’s all the polygon pandemonium we have time for today. But there’s a lot more to say about polygons—so be sure to check back in the future for more.

Following up on our last two Martin Gardner puzzle episodes, if you haven’t yet taken a look at Scientific American's Martin Gardner tribute page, I highly recommend doing so. And while you’re there, you can also pick up a copy of the ebook, Martin Gardner: The Magic and Mystery of Numbers—it’s an awesome collection of Mr. Gardner’s most popular mathematical games and puzzles.

For more fun with math, please check out my book, The Math Dude’s Quick and Dirty Guide to Algebra. And remember to become a fan of The Math Dude on Facebook, where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

Geometric shapes and triangle image courtesy of Shutterstock.