[Math] How do the dimensions of an “infinite” bar of chocolate change?

geometry

Here is a GIF image illustrating a supposedly "infinite" supply of white chocolate.

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After watching this repeatedly, I can't definitively say why it doesn't add up. It clearly can't be infinite and the sizes of the pieces don't seem to be changed/edited. My guess is that the volume of the spaces between pieces somehow adds up to the final piece's volume.

However, the real question I have is: how have the dimensions of the array of chocolate changed? That is, if you start with a $6\times 4$ grid of chocolate pips, what are the final dimensions of the almost complete grid? I figure that height need not be considered because the cuts are made normal to the table surface.

Best Answer

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The ending result is actually 1/5 of a piece shorter than the original bar. That amount(1/5) times 5 pieces across is equal to the extra piece

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