You'll notice that the "whole" triangle is 5-12-13, which is a perfect triangle.

However, the two smaller triangles are 8-3-sqrt(73), and 2-5-sqrt(29). We know the length of the long side of the whole triangle should be 13; however, sqrt(73) + sqrt(29) is not 13, it's about 13.9! What is happening is that the long edge of the first triangle is bowed slightly downward, and the long edge of the second is bowed upwards, the difference being exactly one square.

I think i may have understood how this hollow square happens....let me see if i can put on words...

I got the impression that the main side of the whole figure, the hypotenuse in the 2nd figure is "cutting" the squares in a way the colourful parts is filling less the squares, so the "ghost" one is to compensate for that.


Just a wild guess.

So Sun, my explanation was a rough version of yours? I was kinda right?

Looks like fibonacci sequence. Geometry is cool.

Cool. I'd seen it before but I forgot. You could have also found out by cutting both out, exactly, and placing them on top of each other. Even though that's a bit hard from the computer screen .

groetjes,
Mirella

That explanation is kinda disappointing.

I knew that Jeremy would come into this thread and give the correct answer, and that being only on the 2nd post. So I thought he'd just explain it then lock it like a good Administrator would do

:-p

ZOMG WHERE IS YOUR GOD NOW?

IN MAH PANTS

if you look there is a flash game that lets you do this in a way that makes the difference pretty obvious.

math makes my head hurt