A4 paper

The A series of paper, of which A4 is the most well-known member, is described as being metric. Its dimensions of 210mm x 297mm, don't seem particularly well chosen, but they are actually pretty special.

297 ÷ 210 = 1.41128 = √2

In fact, all of the A sizes have sides that are the ratio 1 : √2. I'll leave it as a simple proof for the reader to show that dividing a page of those dimensions in half will result in two smaller pages with the same 1 : √2 ratio. This is the only ratio which retains its proportion when halved.

Now, looking at the area:
297 * 210 ≈ 62500 = 1000000 ÷ 16 = 1000000 ÷ 2⁴

If you have an A3 page handy you'll find its figures are:
297 * 420 ≈ 125000 = 1000000 ÷ 8 = 1000000 ÷ 2³

If you follow this pattern up to A0 you'll find it has an area of 1000000 ÷ 2⁰ = 1m²

How cool is that!

Wikipedia says that all countries around the world except the US and Canada have settled on A4 as their standard letter paper size, though US letter is in common use in countries neighbouring the United States.



Bonus fact: A6 is commonly used for postcards and toilet paper.