in two sheets that themselves both have an aspect ratio of is proven as follows:

where a is the long side and b is the short side. The aspect ratio for the new dimensions of the folded paper is:

The advantages of basing a paper size upon an aspect ratio of were noted in 1786 by the German scientist and philosopher Georg Christoph Lichtenberg. He also observed that some raw sizes already adhered to that ratio so that when a sheet is folded, the length to width ratio does not

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