Whenever I walk out of a room, what do the people standing about say?
Polly Gone.
And so now we have to talk about it.
Oh yes. The wonderful polygon. It is my favorite shape, you know. Just like Polynesia is my favorite country. And polyester is my favorite material. (Not really, and not really.)
But back to the remarkable polygon.
If you didn’t know, here is what they are. Polygons are a straight-sided plane figure with at least three sides and angles, and typically five or more. You know. Poly equals many.
The word “polygon” stems from two Greek words: “poly,” meaning many, and “gon,” meaning angles.
So essentially, a polygon is many angles hanging out with one another. All the while, they are trying to look organized.
And just like people, polygons come in types. Four of them, in fact.
1. Regular Polygons
These are the overachievers.
Everything matches. Same side lengths. Same angles. No drama.
Like the stop sign. It is that balanced octagon. Symmetrical. Or how about a. baseball home plate? Same angles, lengths, all of that. .
If Polly were a regular polygon, she’d be on time, all lined up and alphabetized. (So yes. Sort of like me.)
2. Irregular Polygons
Once again, a little bit like me, too.
An irregular polygon has sides and angles that don’t quite match up. One side’s longer. One angle’s wider. Disorganized. Apparently, someone didn’t get the memo.
They mostly look lopsided or skewed.
Irregular polygons. I think I have a few of these here and there, in my inner being. A little off, but still holding it together.
3. Convex Polygons
Convex polygons keep everything pointed outward. No dents. No inward folds.
All interior angles stay under 180 degrees.
Think honeycomb cells, tiles, or a cleanly cut gem shape.
Nothing caves in. Nothing turns inward. They seem to be doing quite fine, thank you very much.
4. Concave Polygons
Like a cave. It caves. Concave polygons have at least one angle that caves inward.
You’ll see this in arrow shapes, star outlines, or anything that looks like it has a bite taken out of it.
These types can overlap. Like the home plate? It is both regular and convex.
So there you have it.
Polygons are everywhere. Many angles. Straight edges. And sometimes a bit on the wonky side. They overlap in their characteristics. Once again, just like all of us human beings.
And that, my friends, is about the shape of things.
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“Geometry is the archetype of the beauty of the world.”
— Johannes Kepler
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“Mathematics is the art of giving the same name to different things.”
— Henri Poincaré
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“In all chaos there is a cosmos, in all disorder a secret order.”
— Carl Jung
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“Everything has its beauty, but not everyone sees it.”
— Confucius
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