Kilgore Trout sent thislink over ICQ to me last night. I didn’t have the brain resources necessary to solve it then, and upon looking at it again this morning, I still don’t. Can anyone explain this?
The most rewarding part was when I got my money!
-Dr. Nick Riviera
It’s an optical illusion that can be observed more clearly on paper. The slight curvature of a computer screen obscures the fact that the slope on the top of the group is not a straight line. The two triangle sections do not have the same angles or proportions.
Because of this the upper group has a shallow dip on the upper slope. The bottom group with the “extra” empty square has a hump on the upper slope.
Thanks Padeye… I guess I’ll just have to take your word for it! 
The most rewarding part was when I got my money!
-Dr. Nick Riviera
Specifically, you can see that the green and red triangles are not similar (they’re not just different scales of the same shaped triangle). The ratio of the legs of the green triangle is 2/5, while the ratio of the legs of the red triangle is 3/8. Those ratios aren’t the same.
“If anybody wants a sheep, that is proof that he exists.”
I sent KT a fair warning that I posted this… So he can read this at his own risk!
The most rewarding part was when I got my money!
-Dr. Nick Riviera
Squee, don’t take my word for it. For all you know I could be the head of an evil cabal trying to hide the true secret of the magic triangle. Be more skeptical!
Oh phew, what a relief for you sake. He is a wizard, you know.
“If anybody wants a sheep, that is proof that he exists.”
This easiest way to verify that Padeye is correct is to print out a copy of that image and then take a straight edge and razorblade and try to cut along the tops of both triangles. With the top traingle there’s a concave top, the bottom triangle has a convex top.
I don’t think the similiarity (or lack thereof) of the red/green triangles is an issue.
Well, if you look at the triangle as it cuts through the grid, it seems that it cuts more of each square along the way in the second than it does in the first. In this way the one block gets eaten up and forms the hole.
Jeffery
In one of Martin Gardner’s “Aha” books, he showed several examples of the kind of magic you can do with cutting up stuff and (seemingly) getting different areas.
Interestingly enough, they all seemed to have some kind of Fibonacci connection, as this one did, with one side being 5 and the other 13.
ok, i get it now. with the help of a coworker and lightwave 3D.
so neither of the shapes are triangles.
it all makes sense now.
what is essential is invisible to the eye -the fox