# – How Does The Extra Square Triangle Work?

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I can’t put an image, but I’m talking about that one thing where you have multiple bits that make up a triangle, but if you rearrange them you get the same sized triangle, but with a square now missing.

In: Mathematics

The shapes in the illusion are not true triangles, because the longest side/hypotenuse is slightly curved. The “triangle” with the missing square curves outward more than the other shape, meaning the missing space’s material is instead spread out across the rest of the triangle, making it slightly thicker.

I’m not entirely sure what you’re talking about. Is it like the infinite chocolate bar?

The original triangle and/or the new triangle is not really a triangle. Two of the sides are straight lines, but the third side either bulges in or bulges out depending on how you arrange the pieces. The difference is subtle, but enough to make up the area of the square when it’s spread out over the entire side.

This sounds similar to the “infinite chocolate” illusion, but in reverse. With the “infinite chocolate” illusion:

* You start with a rectangular bar of chocolate, and divide it up into pieces. One of the pieces is a 1×1 square.
* You set the 1×1 square aside.
* Then, you rearrange the pieces to form a rectangle the same size as the original chocolate bar.

You’ll see there:

* a big trapezium, 5 wide, at the bottom, which does not move.
* a 3-wide trapezium and a 2-wide trapezium, that swap places
* a 2×1 rectangle
* the 1×1 square, which gets eaten repeatedly.

The trick is this: although it looks like the pieces fit together neatly after being moved around, they actually don’t . The rearranged pieces don’t make a full rectangle, they make a rectangle with a very thin gap along the diagonal cut. The area of that thin gap is exactly 1 unit. Obviously the gif I linked doesn’t show that.

The version with the triangle probably works similarly – in one arrangement, the pieces don’t quite line up, and there’s a thin gap whose area is the same as the square.