North American Letter size paper is 8 1/2" x 11", an “aspect ratio” of 22/17 or about 1.2941. Is there any other common standard size that is closer to 1/1, or squarer, than this? If there is, my Google-fu fails me; A4 for example is √2 or 1.414. Maybe some notepad size?
How about the three-inch square Post-It notes?
Origami paper is square:
Brian
When I was younger, Quarto was common: 1.23, it was what we used at school. It’s not common anymore. Actually, school notebooks still come in a squarish size, but only for the really young kids (and sort of old people) – the schools switch to A4 notebooks when the kids are large enough to handle them.
I don’t have an authoritative list of broadsheet paper sizes, but Wikipedia has a couple of links claiming that “many U.S. newspapers have downsized to 12 in (305 mm) wide by 22 3⁄4 in (578 mm) long for a folded page.” That means that the unfolded page has a ratio of about 1.05.
It’s common enough for art books to have square pages, so that both horizontal and vertical photographs leave an acceptable amount of white space.
I read somewhere long back that the most aesthetic rectangle is one which has the golden ratio and hence stationery tried to get close to it.
Sometimes, but not always and not exactly:
http://ihl.enssib.fr/en/paper-and-watermarks-as-bibliographical-evidence/the-shape-of-paper
http://ihl.enssib.fr/sites/ihl.enssib.fr/files/J.Lane_graph.jpg
Maybe it is fairer to say there is a band between roughly √2 and roughly golden.
The √2 ratio has a reason: if you cut the sheet in half, the ratio is mantained. Thus the ratio of the two sides of A4 is the same as for A5. If, to take an extreme example, you had the ratio 1:2 and cut the sheet in half, you get the ratio 1:1, when you cut that again in half you get 1:2 again. √2 avoids this oscillation and is thus practical for paper producers.
Yes, that is the basic logic of the “A” line of sheet sizes. It starts with A0, which is 841 × 1189 millimetres and has a surface area of one square metre. With each increment of the “A” number, the size is halved (so A1 is half the size of A0, A2 is half of that again, etc). This neat feature is only possible because of the √2 ratio. It’s also reasonably close to the golden ratio, but that was not the primary concern when the system was designed.
It’s also the logic of the “B” series, except there it’s around having a meter side and fractions of that (at least in the common sizes) .
The “C” series is just weird (but perfect for envelopes)
“A”, “B”, and “C” (as well as D, E, F, G…) papers all have the same shape. It’s just different sizes. C is the mean of A and B.
If you want sheets closer to the golden ratio, it’s not impossible to get some American or Japanese sizes. Also IME every office and of course print shop has a guillotine…
UPDATE: Just today I received a mailing that made me go “wait a minute– am I imagining it or is this larger than usual?”. I measured it and sure enough it wasn’t letter size, it was 9.5x12". A quick bit of Googling reveals that there is a paper size called North American ARCH (short for Architect), the smallest of which is ARCH A at 9.5x12". So OP answered; yes there is an actually standard size squarer than Letter, aspect ratio of approximately 1.263 compared to Letter 1.294
ARCH A is listed online as 9" x 12", for a ratio of 1.333. Where are you seeing 9.5"?
Urgh, I meant 9¼, not 9½. Which throws it all the paper wastebasket. And double-checking you’re right, my own sources says that ARCH A is 9x12". And yet the papers I was sent are definitely wider than 9". The plot (and the paper?) thickens…
If you consider North American paper sizes like ARCH and Letter “standard”, then Japanese AB is no less standard and is squarer than Letter.
We can’t talk about paper sizes and shapes without this nice little video explaining where the “A” type papers come from, but also existentialism of the entire universe
The video keeps calling the standard “metric” even though it only has to do with the Metric system in that the start of the standard is a page of one square meter in area. The real magic of the standard is it’s use of the 1:√2:2 ratio.
There are real standard standards though, namely mainly ISO 269 in this case, which defines sizes A and B. They all have the same aspect ratio.
You never mentioned what you are trying to do, but there are various square notebooks available