Sunday, September 16, 2012

A Strange Polygon

I don't know what a polygon is anymore! I thought that I knew, but it turns out I don't. I mean, a square is a polygon, and so is a triangle. But what about this thing?

Our glossary definition says that a polygon is "a closed 2D shape that has multiple straight (not curved) lines, where every line is touching another line on both ends." And this shape obeys that definition. But it has an infinite number of sides! It also has an inside and an outside, which I guess is important.

What do you think? Is this a monster, or just an unusual example of a polygon?


  1. It depends we want to talk about when we talk about polygons. I suspect that including this as a polygon could mean that in proofs for other problems unrelated to shapes with infinite sides, we'd have to make a special exception about shapes like this. (For instance, we might say something like "This is true for all polygons" but then realize that we have to add "except for polygons with infinite sides." Of course, similar things could happen the other way, but I suspect not as much. But whatever, its just semantics.

  2. Maybe the difference between this thing and a circle is that you can create an algebraic formula to find a given point on this fractal (if you're given the number in an ordered list of this shape, which I believe you can kind of make).

    Well, I can't think about this too much now because I have to write another post thingy.