International Paper Sizes

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We use papers with different sizes for different purposes. Most commonly known is the A4 size paper used for printing with digital printers. There are different sizes conforming to an international standard, designed in 1922 by a German engineer. All the different sizes are inter-related. What is of interest to students of math is that they an unique property related to &radic;2.

The largest size is A0 and each subsequent size is half the area of the previous one. They are successively named A1, A2, A3, A4 etc.

The largest size paper is A0. Its length &amp; breadth meet 2 conditions as closely as possible.

With these conditions the size of the paper comes to be 118.9 cm X 84.1 cm. The area come to be 9999.49 cm square.
 * 1) The area should be as close to 1 sq meter or 10,000 cm square.
 * 2) The ratio of the length to breadth should be as close to &radic;2 as possible.

The significance of &radic;2

Imagine a rectangle whose sides are in the ratio 1:&radic;2. Let us assume the breadth to be &ldquo;b&rdquo; and the length to be &radic;2b.

Now cut the paper into 2 equal halves bisecting the length (i.e the longer side). The side of the new sheet becomes b/&radic;2. We now have another rectangle whose area is half that of the original. Since the sides now are b &amp; b/&radic;2, they are again in the ratio 1:&radic;2!

So by cutting the original rectangle into 2 equal halves, we have got a rectangle which is half the original rectangle and with the same aspect ratio which is 1:&radic;2! Both the rectangles are similar.

This process of halving the rectangle can be continued further and yield similar rectangles with half the area of the previous rectangle.

Having the same aspect ratio across sizes enable enlarging or reducing images from one size to another without distortion.

Other Paper Sizes

So halving A0 gives A1 size. Halving A1 gives A2 etc.

There are 11 sizes – A0, A1, A2, A3, A4 &hellip; till A10 shown diagrammatically.



We can see that this design reduces wastage while manufacturing sheets of different sizes.

Letter &amp; Legal Sizes

Like in the case of the metric system, the US and a few countries have not accepted the above system. The sizes Letter &amp; Legal are used in the US.

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