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The Morning GIF: New math

Fibonacci Bamboozlement will have you scratching your head.


Lorraine Murphy


Posted on Jul 18, 2012   Updated on Jun 2, 2021, 2:20 pm CDT

Here at the Daily Dot, we swap GIF images with each other every morning. Now we’re looping you in. In the Morning GIF, we feature a popular—or just plain cool—GIF we found on Reddit, Canvas, or elsewhere on the Internet.

Sometimes things just don’t add up. This, my friends, is one of those times.

It seems so simple: a square is divided up into smaller squares, eight on a side, making 8×8 or 64 small squares. A few straight lines are cut through the array, the pieces are rearranged, and now they form a rectangle five squares high and thirteen squares long, or 5×13 or 65 small squares.

Wait. What?

Yes, a new square has apparently been created out of thin air.

The trick even works in reverse: There’s apparently a way to arrange the pieces so that they total to 63 instead, although the javascript that makes the magic work appears long-dead.

Ladies and gentlemen, you have become victims of the infamous Fibonacci Bamboozlement. Simply put, the long edges of the triangles are so long that even a slight change in their angle has a cumulatively large effect, seeming in one case to create a new square, and in another, to remove one, while what is actually going on is nothing more than the creator fudging the way the pieces fit together. They appear to fit perfectly, but in fact are slightly off, which is just enough of a difference to account for the area of one square, plus or minus. There’s a bar bet to be won in there somewhere.

The Fibonacci Bamboozlement (that is its actual name) was first uploaded to the Internet in 2004, at the now-deceased blessa.com, and then it was linked and discussed on Reddit-predecessor Metafilter.

We found a working model on Bits and Pieces, and have it here for your delectation and puzzlement. And if you figure out how to set up that bar bet, we’d appreciate hearing back. Just for informational purposes, of course.

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*First Published: Jul 18, 2012, 7:48 am CDT