I was listening to a podcast (it's podcast 10, and here's the transcript on his blog) by the artist Danny Gregory (ok - more like I overheard my wife listening to it and my ears perked up when Danny started talking about the mathematical development of the A, B, and C paper sizes). He said that an A0 piece of paper is defined as being 1 metre squared with the sides of the paper having a ratio of square root 2 : 1 (rounded to the closest millimetre). What are the sides of the paper?
This question is related to the one regarding the folding of A, B, and C series paper and the holding of the square root of 2 : 1 ratio.
Answer
1189 mm X 841 mm
Analysis
Let's first remember that the area of a rectangle can be found by multiplying the base times the height:
A = bh
We're told the area of the paper in metres. Let's convert that to millimetres:
1 m^2 = 1 m X 1 m = 1000 mm X 1000 mm = 1,000,000 mm^2
With the sides of the paper, we know the ratio is square root 2 : 1. We'll need a variable, x, to make sure we count the same amount of 1's as we do square root 2's:
The short side is 841 mm. The long side is:
These are both in millimetres.
And now let's see just how big the paper really is (in millimetre squared):
and so just a wee bit smaller than the defined size!
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Questions and comments always welcome!
