I think we figured it out. If you look at the two triangles (green and red), they have different slopes. One is 2/5 and the other is 3/8. So if you switch them around, the slope is changing constantly.

You can also tell that the spacing on the diagonal like (the white in each square) is not the same as the top one.

that's my guess

I'd agree with the first part of your solution. The gradients are different and therefore the two composite figures that look like triangles are not actually triangles at all. The hypotenuses are not straight lines but each have an angle to them, one inwards and the other outwards. Therefore there is a difference in the space used. And in this puzzle seems to be exactly 1 square.

Warot is right. I put the images on top of each other and got this result:

Optical illusion is all... your eye cannot really differentiate the slope. Otherwise, it is mathematically impossible.

If you pay attention, you can definitely see that it is not a straight line. But being an engineer, I did rise / run

Very impressive guys. I couldn't figure it out myself. Now that I see that the slopes are different, it makes a world of a difference.

After obsessing over this puzzle for about an hour, making my own diagrams etc. ...I totally agree with you donau.

I really like these types of mathematical puzzles. An interesting thread DocM

I also like this kind of brain gymnastics. I've always been kinda fond of it but lately I like them even more because I think doing little things like this might help keep bigger problems at bay (referring to memory loss etc.).

nice to see that we have some people who like to use their heads on this forum,
I didn't waste a lot of time on this puzzle , but thought that some of you might like to give it a shot...I'll try to find more of this kind of stuff if you guys are into puzzles of that sort