Well, if you’ve seen the previous posts, you’ve probably figured it out already but here’s my attempt to make it more obvious.
The only things that matter to understand the “trick” are the two triangles. The original two triangles are at the top in this image.
The big triangle is wider per tallness as compared to the small triangle. In other words, if it was the same height of the small triangle it would be wider. So let’s exaggerate that by keeping the 8 wide but make it only 1 high instead of 2.
The small triangle is narrower per tallness as compared to the big triangle so let’s exaggerate that by keeping the 5 wide but make it 3 high.
If we put them together in the same way you get an exaggerated picture of what’s going on if the original. That’s the second set in the image.
Now switch them the other way and you see an exaggerated picture of the bottom triangle in the original. That’s the third set.
Now, what I should have done the first time is superimpose the original two triangles and that’s what you get in the bottom set. It’s pretty obvious there that the two triangles are actually different shapes and not true triangles and that difference is where the “extra” space comes from. This explanation was the one that did it for me.
I don’t buy it. I don’t buy this explanation or this one.
So I made my own little blocks in Excel and copy/pasted them, moved them around, and, I didn’t pay too much attention to the joints lining up but, it’s obvious that the same blocks have two different areas. No matter how you count it, the area of the triangle is 5 blocks X 13 blocks / 2. And the area of the first is the same as the area of the second with one block missing. Using the same pieces.
There are no curves and the pieces are the same size and cover the same area minus one block.
I don’t get it.