Can someone explain to me (on a mathematical or geometric basis) what happens in the following video or is it just a magic trick? Thank you.

http://www.youtube.com/watch?v=3PszMaZ5Ipk&feature=player_embeddedheltruuk?

## Answer

Dear Gerard,

This is of course a magic trick, and you can very well see how the magician outwits his audience. Freeze the video at 55 seconds. Now count the number of blocks in the depth. That should be nine, but you can see that on the slanted line closest to the “magician” there are blocks that are just a bit longer than a square (i.e. rectangular). And indeed, the video is continuous until when the man removes the blocks from the frame, then it seems as if the camera is turned off and on, and two videos are welded together. So the lower half is then replaced by a slightly longer lower half, but that is not very noticeable, because it (1) is only slightly longer, and what is added (the area of â€‹â€‹three squares) is divided over seven squares (the entire width) and (2) the block is cut diagonally, and then irregularities are less noticeable than when something is “straight-up” wrong. In any case, this camera trick has made the block bigger, and then three squares can disappear from it. It would have been more subtle to make just one block disappear, then the increase in size is less noticeable.

The “bevel” of the fault line also aims to make exactly one block disappear with each step. The slope is chosen in such a way that with each step, by sliding the blocks, the elongated blocks in the middle become less elongated. You can see this by comparing the rightmost elongated block with the leftmost elongated block at 55 seconds: the former is longer below the fault line than above it (below from the man’s point of view), while this is just the other way around at the leftmost (left from our point of view).

By the way: there is a similar trick with a 7 x 9 rectangle cut in such a way that, after rearranging the pieces, an 8 x 8 board appears… But some squares are then slightly rectangular, inconspicuous.

In the second part of the video, the reverse happens: the camera is again discontinuous when the pieces are removed from the frame (at 2 minutes 22 seconds), and freezes the image at 2 minutes 36 seconds: count the number of blocks the depth, you see that there are less than nine: in the middle some of them have shrunk.

Conclusion: a camera trick that counts on us not to freeze the frame to expose the trick. It’s not even a magic trick, because it doesn’t require any skill on the part of the performer (other than making the pieces), and it can’t be performed “live” because pieces need to be swapped.

I hope this clears up some of the mystery.

Regards,

— Hendrik Van Maldeghem

## Answered by

#### prof. Henry Van Maldeghem

Mathematics, geometry, algebra

http://www.ugent.be

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