It took about 10 minutes for me and PeZook to crack this one, but we are no mathematicians I guess anyone who deals with this stuff on a daily basis will crack this in no time. But please post your explanations in spoiler brackets Also, if somebody knows this, don't be a game breaker
It's one of those ones where the slope of the triangles is slightly different, but the human eye is stupid, and assumes that they're the same when they merge into each other. This means that we don't notice that the triangles in the top picture develop a slight kink in their hypotenuse in the bottom picture (which means that they are no longer triangles, but rather have turned into quadrilaterals.
There's another similar problem hanging around where the "triangle" rebus in the first picture develops a hole after its constituent shapes are shuffled around a bit.
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"Why does it look like you are in China or something?" - havokeff
It's cute. I remember this puzzle from an old book I learned algebra from back in seventh grade. I tried making cut-out pieces too, but that turned out to be harder than drawing it (for the same reason that resolves the puzzle).
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There was a similar puzzle posted some years back, I think by Boyish Tiger lily. Like Lusy Chan I suspected the same solution. The only problem is I am finding it harder to prove that Spoiler
those "triangles" are really quadrilaterals which just look like triangles using trigonometry. Then I got bored.
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Australia, Canada, China, Colombia, Denmark, Ecuador, Finland, Germany, Malaysia, Netherlands, Norway, Singapore, Sweden, USA.
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Oh wait, I just realised how I could show my hypothesis. Spoiler
Just look at the bottom triangle in the 8 X 8 square. Take the far right angle and call it x. Tan x = 3/8. Now draw an imaginary horizontal line starting one square above the base of that triangle. This line is obviously parallel to the base. Now lets call the new angle formed from this new line and the hypotenuse angle y. If this shape was a triangle, then Tan y = 3/8 (or some other equivalent fraction). It does not. The opposite length over adjacent is 2/5. Ergo its not a triangle, and thus neither is the "triangle" above it. So I bet you those other 2 "triangles" in the 13 X 5 shape are slightly bigger, hence giving the extra 1 square.
Never apologise for being a geek, because they won't apologise to you for being an arsehole. John Barrowman - 22 June 2014 Perth Supernova.
Countries I have been to - 14.
Australia, Canada, China, Colombia, Denmark, Ecuador, Finland, Germany, Malaysia, Netherlands, Norway, Singapore, Sweden, USA.
Always on the lookout for more nice places to visit.
The way I determined it was to just count the squares up and down. For the "triangles" in the second picture, the bit closer to the point goes two to the right and five up, for a slope of 2.5, while as it gets wider, the edge goes one across and three up, for a slope of 3.
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- Darth Wong Free Durian - Last updated 27 Dec
"Why does it look like you are in China or something?" - havokeff
Assuming that all four shapes are consistent between both pictures (the assumption we're meant to make), then the slope of the angled line of each of them should be the same! Rise/run = slope. 13/5 = 2.6 would be the slope for both of the non-triangles' angled line as well as the triangles based on the bottom-right image. But the picture at the top-right clearly shows the slope is 5/2 = 2.5 for the 'bulky' pieces and 8/3 = 2.33 for the triangles (once you turn them around). Thus, these shapes are NOT the same shape between each picture and will have different areas.
Though how it manages to look so clearly correct is kinda beyond me right now. Time to check the other answers .
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Same deal as in the picture someone posted a while back, something that looks like a triangle at a glance actually isn't. The hypotenuses of the would-be triangles in the lower image aren't straight.
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It worked for me. I wondered "Why was it hard to cut out? Looks simple", and then I looked a bit closer. I had actually disregarded the fact the centre line in the second shape looked a bit crooked as an optical illusion, until I started counting off the rise and run.
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The first set of wedges have slopes of 3/8 each, but the second set have two slopes, a slope of 1/3 for the 3 squares where they touch, and a slope of 2/5 where they don't. This changes the area of each wedge from 12 to 12.5. The 2 trapezoids are unchanged in area.
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I used trig to determine the precise angles of the triangles, and discovered they didn't quite add up for the second shape. It's kinda fun to see how other people approach the problem: Tolya used a simple ruler and immediately saw the problem
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I used trig to determine the precise angles of the triangles, and discovered they didn't quite add up for the second shape. It's kinda fun to see how other people approach the problem: Tolya used a simple ruler and immediately saw the problem
Spoiler
From viewing it with my naked eye, the triangles already looked funny. However it took me a bit longer to figure out how best to prove my hypothesis. The other option of course is to save the picture on your hard drive, and then magnify it, where it should be more obvious.
Never apologise for being a geek, because they won't apologise to you for being an arsehole. John Barrowman - 22 June 2014 Perth Supernova.
Countries I have been to - 14.
Australia, Canada, China, Colombia, Denmark, Ecuador, Finland, Germany, Malaysia, Netherlands, Norway, Singapore, Sweden, USA.
Always on the lookout for more nice places to visit.
As a square, it has an area of 64
Re-arranged as a rectangle, it has an area of 65 Re-arranging a shape does not change the total area
Explain the discrepancy.
“I am the King of Rome, and above grammar”
Sigismund, Holy Roman Emperor
Though how it manages to look so clearly correct is kinda beyond me right now. Time to check the other answers .
Spoiler
It looks convincing because the shapes' outlines are thick enough, relative to the discrepancy, to hide what would be empty space if they were razor thin. There's only one square spread out over the 14 unit "hypotenuse"; the lines look like they're about 1/6th the length of a square.
Like other people mentioned, the easy way (that I used) is to notice that 5/2 does not equal 8/3 and then, if you feel like it, calculate the area of the gap.
It took about 10 minutes for me and PeZook to crack this one, but we are no mathematicians I guess anyone who deals with this stuff on a daily basis will crack this in no time. But please post your explanations in spoiler brackets Also, if somebody knows this, don't be a game breaker
Spoiler
If the tan shapes in the leftmost image had been cleanly transferred to the one on the right, then the line bisecting the two would be straight. It's imperceptibly crooked, though, which means the shapes are not identical. More specifically, the tan shapes on the left are two triangles, while the similar-looking versions on the right have four sides.
Björn Paulsen
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I guess anyone who deals with this stuff on a daily basis will crack this in no time. But please post your explanations in spoiler brackets 
.
"DO YOU WORSHIP HOMOSEXUALS?" - Curtis Saxton (source)
- PeZook
