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
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.
Here’s an example: [https://www.reddit.com/r/interestingasfuck/comments/jcsaql/this_is_a_reprresentation_of_the_banachtarski/](https://www.reddit.com/r/interestingasfuck/comments/jcsaql/this_is_a_reprresentation_of_the_banachtarski/)
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.
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