4 ms·

When someone claims uncritically that the ratio of any two integers is √2, I get a little edgy. I'm also having a hard time following this simplification:

When someone claims uncritically that the ratio of any two integers is √2, I get a little edgy. I'm also having a hard time following this simplification: A / √A = A × A / A = A Huh? This only holds if √A = A = 1. I haven't checked the rest, but this doesn't give me much confidence. Of course, knowing those Europeans, these sizes do probably make tons of sense on paper (see what I did there?), even if this isn't the best explanation of it.

talideon 12y ago
There's nothing crazy here. It just means that if the length of the long side is √2 times the size of short side. That has the nice property that you can bisect the sheet and get two smaller sheets where the ratio between the long and short edges is maintained, which makes it standardising a whole bunch of other things much more straightforward.
- amalcon 12y ago
  I believe that gp's point is that this is impossible, what with √2 being an irrational number. It is pretty close (4 significant digits), but of course not exact.
  - talideon 12y ago
    It's not that big a deal: once you have a basic page size that's close enough, it's just a matter of slicing it in two. In practice, any error is too small to matter.
delinka 12y ago
The article's not claiming that the ratio of any two integers is √2, he's claiming that when the ratio of the lengths of the sides (the aspect ratio) is √2 that it's easy to keep that ratio with smaller pages by cutting the longer dimension in half. As for your equation above, A/√A != A x A / A, but I'm not seeing where in the article you got this either.
- deleted 12y ago
  [deleted]
- baddox 12y ago
  > The size is 210 mm × 297 mm and has a ratio of √2 (math!). That looks like a claim that the ratio of two integers is sqrt(2), but it's fairly obvious that he really means that it's very close.
  - delinka 12y ago
    I don't think anyone would attempt to assert that any measurement (or ratio of measurements) made with our current technology could ever be precisely √2 or even π (that's pi)
gearhart 12y ago
He's written A / √A = A × A / A = A, but what he means is A / √A = √A × √A / √A = √A, which is actually true and is what he uses below
- philsnow 12y ago
  another way of writing the same thing is A / A^(1/2) = A^1 * A^(-1/2) = A^(1 + (-1/2)) = A^(1/2)
lmm 12y ago
Of course 297/210 isn't (and can't be) exactly sqrt(2). But it's very close (4 s.f.), and the important property works: 420/297 is again not exactly 297/210, but it's well within the tolerance for most use cases. (I can't load the page to check what it's doing with this simplification).
theoh 12y ago
There is a very simple rule for the size of the A series pages. Markus Kuhn covers it here: http://www.cl.cam.ac.uk/~mgk25/iso-paper.html http://www.cl.cam.ac.uk/~mgk25/iso-paper.html Basically, in metres the An page dimensions are pow(2, (plus or minus)1/4 - n/2) and always round down to the nearest mm.

talideon 12y ago

There's nothing crazy here. It just means that if the length of the long side is √2 times the size of short side. That has the nice property that you can bisect the sheet and get two smaller sheets where the ratio between the long and short edges is maintained, which makes it standardising a whole bunch of other things much more straightforward.

amalcon 12y ago
I believe that gp's point is that this is impossible, what with √2 being an irrational number. It is pretty close (4 significant digits), but of course not exact.
- talideon 12y ago
  It's not that big a deal: once you have a basic page size that's close enough, it's just a matter of slicing it in two. In practice, any error is too small to matter.

delinka 12y ago

The article's not claiming that the ratio of any two integers is √2, he's claiming that when the ratio of the lengths of the sides (the aspect ratio) is √2 that it's easy to keep that ratio with smaller pages by cutting the longer dimension in half. As for your equation above, A/√A != A x A / A, but I'm not seeing where in the article you got this either.

deleted 12y ago
[deleted]
baddox 12y ago
> The size is 210 mm × 297 mm and has a ratio of √2 (math!). That looks like a claim that the ratio of two integers is sqrt(2), but it's fairly obvious that he really means that it's very close.
- delinka 12y ago
  I don't think anyone would attempt to assert that any measurement (or ratio of measurements) made with our current technology could ever be precisely √2 or even π (that's pi)

gearhart 12y ago

He's written A / √A = A × A / A = A, but what he means is A / √A = √A × √A / √A = √A, which is actually true and is what he uses below

philsnow 12y ago
another way of writing the same thing is A / A^(1/2) = A^1 * A^(-1/2) = A^(1 + (-1/2)) = A^(1/2)

lmm 12y ago

Of course 297/210 isn't (and can't be) exactly sqrt(2). But it's very close (4 s.f.), and the important property works: 420/297 is again not exactly 297/210, but it's well within the tolerance for most use cases. (I can't load the page to check what it's doing with this simplification).

theoh 12y ago

There is a very simple rule for the size of the A series pages. Markus Kuhn covers it here: http://www.cl.cam.ac.uk/~mgk25/iso-paper.html http://www.cl.cam.ac.uk/~mgk25/iso-paper.html Basically, in metres the An page dimensions are pow(2, (plus or minus)1/4 - n/2) and always round down to the nearest mm.