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

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

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.

• generally, if you carefully draw (including finding the slopes of all relevant line segments) you find that the after picture has a slim empty part, probably triangular here – Will Jagy Jan 9 '15 at 2:23
• en.wikipedia.org/wiki/Missing_square_puzzle – Deepak Jan 9 '15 at 2:23
• What makes it an infinite bar of chocolate? – Ross Millikan Jan 9 '15 at 3:15
• @RossMillikan Presumably, the OP meant inexhaustible (in supply) and not infinite (in span). – Deepak Jan 9 '15 at 3:54

• This variation is very interesting. It is nice to see that the extra piece's area is easily verified. But what about the $6\times4$ case above? That one interests me more because the "perforated" lines seem to match up better all around. – Xoque55 Jan 9 '15 at 2:42