Hy people! I have just received this image from my brother via gmail. We had very similar mathematical optical illusion at the very start of this website, and I find this kind of illusions hardest to solve. Maybe this should belong to some new category called “Brain Teasers” or “Mighty Puzzles“, still we can probably pull this one of as part of the illusion site as well. So, the question follows: if all the shapes that form these two rectangles below, are of the same shape and areas, how come the overall surface of the second is bigger? Where is the mistake? How do you explain this one?
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This one is a bit weak. It is obvious to the eye that both triangles on the right do not build a straight line. In fact, those are not triangles, they are “quadrangles”.
Hey, Black Mamba, thank you very much. I have a poor English and I was very tired to look for a dictionary. ;)
I think there is hole in the middle – very long and very narrow.
Ok. Here’s where I found the problem.
The top of the quadrangle equals exactly 3 squares. At the cross section of the triangle where the top of the quadrangle meets. it should equal 2. (2+3=5). If you look at the 8×8 square, The cross section of the triangle at that point is clearly less than 2 squares. I think that’s a sound explanation.
If you actually try to cut up an 8×8 square that way and rearrange the pieces, there’s a really thin hole in the middle of the rectangle which has an area of 1.
I think that explains it.
This one’s just stupid. It’s not an illusion at all, just very sloppy drawing.
There’s a thin parallelogram in the core of the right-side shape, which is 0.117 units wide at it’s thickest. The heavy line weights in this picture help to obscure its presence. They’ve also fudged the shape of the yellow triangles on the right to further obscure it.
Essentially, the ‘diagonal’ lines in the left-side shape are not perpendicular to each other. Instead of 90°, they are 88.7546°. This means they are not collinear in the right-side shape, as you would assume. This creates a 1 square unit parallelogram.
dude,weird post