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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,
October 7, 2016
Episode #221

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Geometric ShapesQuestion: What do you say when you see an empty parrot cage?

Answer: polygon.

Ha!

OK, so it’s not exactly the greatest joke in the world, but geometry is not exactly a hilarious subject. Beautiful, elegant, perhaps picturesque, but not traditionally full of funny. So we can’t be too picky, can we?

The word polygon is probably one of those words you know you’ve heard before, but you’re really not sure where that was, when that was, or what it actually meant. Sure, you probably have an intuitive feeling that polygons have something to do with geometry and shapes, but what exactly?

Lucky for you, that’s exactly what we’re talking about today..

What Is a Polygon?

The logical way to begin our look at the mighty polygon is to first figure out what the word “polygon" means. A lot of you will be familiar with the first part of this word—poly—which derives from the Greek word for “many.” So a polygon is many somethings…but what?

Of course, that’s where the “gon” part of polygon comes into the story. In particular, “gon” is part of a Greek word that means "angle" or "corner." So polygon means “many angles” or “many corners.” And that's exactly what geometric shapes known as polygons contain.

Polygon means "many angles" or "many corners."

A bit more formally, a polygon is defined as any closed two-dimensional shape made up of several straight line segments (and thus also many corners). The “closed” part of this definition means that the line segments must eventually come around and connect together to form a closed chain. The two-dimensional part means that polygons must lie entirely in a flat plane like a sheet of paper.

Importantly, all of the line segments in a polygon must be straight…they can’t be curved. So a circle—or any other curved shape—is not a polygon.

And that’s it! Each and every one of the myriad shapes that satisfy these conditions is a polygon.

Regular and Irregular Polygons

There are lots of ways to further break up the infinite variety of all possible polygons into different categories. One important distinction is made between what are known as regular and irregular polygons.

Polygons whose sides are all equal in length and whose angles are all equal in size are known as regular polygons. These are some of your favorites. The three equal sides and angles of an equilateral triangle, the four equal sides and angles of a square, the five equal sides and angles of a pentagon, the six equal sides and angles of a hexagon, and so on, mean that all of these shapes we know and love are regular polygons.

Triangle

Of course, not all polygons are regular. For example, rectangles, rhombuses, most of the triangles in the universe (besides equilaterals), and a whole mishmash of other possible polygonal shapes are irregular if their sides and/or angles are not all equal.

In the world of all possible polygons, irregular is actually the norm—it’s the few-and-far-between very special regular polygons that are actually the oddballs.

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