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The first video in post #274 looks legit -- but unfortunately, it's not.  It involved some trickery on two counts: (1) careful film editing, and (2) replacement of pieces between "cuts".

 

In terms of the first, this is at least two, and possibly, three recordings which are spliced at specific times to give the illusion of one continuous set of actions. In particular, right after the "cut line" is shown and the cut it made, some time elapses (long enough to replace the pieces in the video with different pieces), and that time is removed through editing.

 

In terms of the second, when the cut is made, it is from the top left of the second row of rectangles to the top right of the third row of rectangles.  The angle of the cut is important because, if you look closely, it bisects the height of the third row of rectangles.  This effectively removes 1/4 of each of the rectangles when the pieces are separated. This would leave you with 1/4 less area when the pieces are reassembled -- with one rectangle left over.  Which is what, in reality, it does.

 

But ... if you watch the video, you appear to have the same complete set of rectangles when the three pieces are reassembled, with the "extra" piece being placed with the other pieces.  This gives the impression that you could do this sequence over and over, eventually filling up a container with the removed single rectangles -- all the time, retaining the original size and shape of the complete set of rectangles.

 

This is of course, impossible.  And, I'm going to tell you how it was done ...

 

If you try this yourself, when you reassemble the pieces, you will notice two differences from the video:

1) The third row of rectangles is now shorter than the other five rows!  In fact, it is now 1/4 shorter.  IF you look at the left column of rectangles on the larger piece that is cut (the right-hand piece), you will notice that the bottom left rectangle is not the full height of the others.  That's because you cut off 1/4 of the height when you made the angled cut. You'll note that in the video, the third row, when the cut pieces are reassembled, is the same height as the other rows.  This is geometrically impossible -- since you removed 1/4 of the height.

2) When you add the left-most piece you cut back on the right side, you'll see there's no lower horizontal line on that piece.  That's because when you made the cut on that piece, you started at the horizontal line on the lower left.  You'll note, that in the video, this upper-right column had four horizontal rows.  This is geometrically impossible, because when you made the original cut, there was no bottom row remaining on the piece.  Look at it before you move it around, just after you make the cut, and that will confirm what I said.

 

So basically, the way the video is made is through cheating, as follows:

1) The cut is made as indicated

2) The cut pieces are removed and replaced with other pieces -- which have two differences from the original ones.  First, the lower row is 1/4 higher than the cut pieces.  This extra height is needed so that when reassembled in the new locations, the rows then all have the same heights. Second, the column that goes on the upper right is replaced with another piece where the cut was actually made 1/4 of the height BELOW the lower horizontal border.  That is necessary so the new piece still has the lower horizontal row on it.

3) The video is edited to remove the time and actions of replace the original cut pieces with the new "doctored" pieces.

 

IF you watch the video closely, you'll see the height of the whole set of rectangles suddenly increase after the cuts are made -- that's because the new, larger pieces have been inserted.

 

Sorry, looks cool but it involves trickery to make it happen.

 

Don't believe me!  Try it yourself and notice how the end result looks quite different from the video.

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