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        riddles >> general problem-solving / chatting / whatever >> A4 Paper Size
        
(Message started by: Barukh on Oct 19^th, 2004, 2:07am)

Title: A4 Paper Size
Post by Barukh on Oct 19^th, 2004, 2:07am

A friend of mine asked recently the following simple question: Why the dimensions of the A4 Paper format are what they are? I didn't know the answer - until he told me.

Do you know the answer?

May be, you have other questions of that kind?

Title: Re: A4 Paper Size
Post by towr on Oct 19^th, 2004, 3:57am

::[hide]
The ratio between the sides is 1 to sqrt(2)
This means that if you fold it in half, the ratio remains the same. And that's all sorts of wonderful. If you have an A3, you can make 2 A4's out of it, or vice versa: f.i. print an A3 image on 2 A4's and put those together.

That covers the relation between width and height. The absolute values depend on the area, and again it makes perfect sense:

A4 = 0.0625 m²
A3 = 0.125 m²
A2 = 0.25 m²
A1 = 0.5 m²
A0 = 1 m²

So an An size paper has area 1/2ⁿ, and since weight of paper is given per area-unit, this makes it easy to calculate.
an A4 of 80 gr/m² paper weighs 1/16th of 80 gr = 5 gr
[/hide]::

Title: Re: A4 Paper Size
Post by Grimbal on Oct 19^th, 2004, 10:28am

So the answer would be [hide]sqrt(sqrt(2))/4 m and 1/sqrt(2) times that, that is 29.7 cm x 21.0 cm.[/hide]

Title: Re: A4 Paper Size
Post by towr on Oct 19^th, 2004, 12:42pm

That's an answer to the question of what the dimensions are, not to why they are what they are.

Of course metaphysically speaking, they are what they are because if they were not, they would be what they aren't, which is a contradiction. So they have to be what they are because they cannot be anything else.
hmm is that assuming they are in the first place?

Title: Re: A4 Paper Size
Post by Sir Col on Oct 20^th, 2004, 12:58am

And of course, your deductive reasoning depends on the state of being and not being, being mutually exlusive, as opposed to existence of some state in-between. Whether or not something can be between being and not being depends on being sure that being and not being exist as mutually exlusive entities and the certainty that things that are, are what they are. As we cannot be sure of this, the state of in-betweenness must be a potential of all things. Perhaps it IS the state of all things?

By the way, nice expo on the family of A_n papers, towr.

Title: Re: A4 Paper Size
Post by Grimbal on Oct 22^nd, 2004, 4:56am

More about the An paper sizes.

http://www.cl.cam.ac.uk/~mgk25/iso-paper.html

What I didn't know is that the B and C series are also related to the A's.