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Edit made on February 25, 2019 by ColinWright at 13:02:44
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HEADERS_END
[[[>40 IMG:A4paper.png ]]]
All A grade sheets of paper are rectangles whose sides are in the ratio EQN:\sqrt{2}:1.
The area of an A0 sheet is 1 square metre.
Folding an 'Ax' sheet of paper in half produces an 'A(x+1)' sheet.
Therefore, the area of an 'Ax' sheet of paper is EQN:(\frac{1}{2})^x square metres.
The actual dimensions of A4 are 297 mm x 210 mm. We can compute the dimensions as EQN:\frac{250\sqrt2}{sqrt(\sqrt2)}
EQN:\left[\frac{250\sqrt2}{\sqrt{\sqrt2}}\right] mm and EQN:\frac{250}{sqrt(\sqrt2)} mm that's EQN:\left[\frac{250}{\sqrt{\sqrt2}}\right] mm,
which are 297.3017 ... mm and 210.2241 ... mm. mm respectively. Very, very close.
The ratio of sides is an irrational number, just as for a golden rectangle.