This writeup contains the solution to
Triangle Challenge. If you haven't seen that node, I suggest you start there.
I'm ready to read the solution!
Right, you have come here because you've cracked the Triangle Challenge, or you've simply given up. So, what's up? Well, let's just start by saying that I fooled you a bit. You have in fact not made the same triangle, but one which is slightly bigger. In fact, it's exactly 2 squares bigger; the extra space in the middle.
How did you do that?
Well, if you look closely at the figures, you discover that the triangle isn't really a triangle at all. (Oops, I guess I lied again, dammit!) The original "triangle" is slightly concave, which you can see by the fact that 11/8 > 4/3. In other words, the slope of the 11/8 piece is steeper than the slope of the 4/3 piece. The second "triangle" is then slightly convex. You would also see this if you cut out the pieces accurately, but not if you are just a bit sloppy.
So what's clever about this, then?
Well, you might say "nothing". I would disagree. I agree, the challenge was really a bit unfair, since I was lying to you in the first place. But you should have been able to see that, so what are you whining about? :)
What I find brilliant about this, is how the extra space makes up exactly two squares in the middle. It's actually quite well made (did I tell you I didn't make it?). I hope you had as much fun pondering it as I had.