Nitpick: typo in the dimensions for A3.
Better than an average square, better than an average ruler.
Everyone makes paper the same hypothetical way, by producing large sheets and cutting them in half, and ANSI E (34"x44" or 864mm x 1118mm) isn't that different than A0 (841mm x 1189mm), but the slight starting difference means that there are two aspect ratios for ANSI (17/22 and 11/17). On the one hand, they're simple fractions and not irrational numbers; on the other, they're different, so you can't just double the size of something printed on ANSI A/letter sized to fill ANSI B/tabloid size, the way you can go from A4 to A3.
Only a small subset of users will ever want to do that (since if you're printing text you probably need to re-typeset it to keep the type a good size for reading), but only a small subset of users actually care about the aspect ratio or exact dimensions of their paper at all, so whether it is 8.5 or 8.11 or 8.314159... inches doesn't really matter.
Teachers at school would print (or photocopy) A4 in half to save paper, or doubled for the blind girl in my class.
I'd do it myself at university to save paper (money).
I don't print much nowadays, but I use this feature occasionally to print something as a booklet. I printed some lost board game rules on A3, since it was an A4 PDF.
People do that all the time with US letter paper, print two to a sheet, you just end up with slightly wonky margins and usually everything being more like 40-45% the size it would be doubling up A4 paper. That use case isn't really hindered.
Every printed document, almost without exception, is printed on larger sheets which are later folded and cut.
Being able to do this precisely saves a vast amount of waste and time.
ANSI A (US letter) is a half sheet of ANSI B (ledger/tabloid) is a half sheet of C is a half sheet of D is a half sheet of E. When producing the paper, there is no waste of material or time, its the same process just starting with a slightly differently sized starting sheet (hypothetically; I am assuming that paper production has advanced beyond shaking screens of the largest handleable size by hand).
The difference is that ANSI A, C and E have aspect ratios of 17/22 (0.77) and ANSI B & D have aspect ratios of 11/17 (0.65), while all ISO sizes have aspect ratios of 1/sqrt(2) (0.71).
The waste comes in when scaling between adjacent sizes.
Going from A4 to A3, you can enlarge a document to 141% of the original size, and the margins will match.
Going from US letter to tabloid (ANSI A to B), the width of the paper is 129% larger and the height is 154% larger, so you can only enlarge your document to 129% the original size, and you have larger vertical margins, which is waste.
(But if you double it, from A to C, the problem goes away, because the aspect ratio is the same; so you can produce posters of multiple sizes, just not on every ANSI paper size at once.)
Regardless of the size of your printing sheet, you choose a page size that's based on dividing your printing sheet in half N number of times, typeset your document to that page size (which you can't even skip for ISO paper sizes, because you pick your font size independent of the paper sizes), print 2^N pages per printing sheet in a particular pattern, fold and/or cut the sheet up, and bind.
There's no difference in waste or time regardless of your paper size choices, unless you do something silly or artistic, like choosing to print a square book or some shape not derived from halving your paper size.
[^1]: This is fun! https://papersizes.io/us/
Not as a consumer. As a paper producer, you take advantage of it by cutting large sheets of paper in half to produce smaller sheets. Since you never sell any sizes that aren't clean multiples of each other like this, you've minimized the amount of paper you waste. That's the "advantage".
This was once the standard way of making paper; I don't know if it still is.
I’m sure you can do that on other size systems, but ISO paper sizing gives you accurate scaling.
Same goes for photocopies, photocopiers can scale copies so two A4 sheets copy to one, if you don’t need the same size.
This assumes there are no errors anywhere in the sizes or alignments of the A4 base page or either A5. Otherwise, you'll have an A5 running over an edge of the A4 or both A5s overlapping in the middle.
If your pages are designed with margins on the assumption that errors in the paper are common, this issue disappears because the margins cover for it. But still, if I wanted to do a display of two 8.5" x 11" sheets of paper, I'd want a board that was bigger than 17" x 11".
For commercial printing, there's the SRA paper series (Supplementary Raw) which is designed to accommodate bleed and alignment bars. An A4 glossy magazine, for example, might be printed on SRA3 and will be trimmed, folded, and stapled automatically at the end of the printing process. But that's a technical detail for the printer to care about - the publisher or designer might specify "folded A3 with bleeds", and the printer will choose the correct raw format to provide that within their printing system.
Fold an 8.5" into a square (right triangle) and the long edge is exactly 12.02"
Fold that in half and you can measure 6.01", and 3.005" (exactly). You get 1.5" for free, and can fairly accurately get exactly 1" by rolling the other 3" side into thirds.
If you want to get an exact 1", you can technically get there via 11"-8.5"-1.5", and that gives you the full imperial (fractional) measurement basis, all from folding a (presumably accurate) 8.5x11" piece of paper.
Because A0 is defined as having an area of exactly 1 square meter, the paper density (GSM or grams per square meter) maps directly to the weight of the sheet.
>A0 = 1 meter square.
>Standard office paper = 80 gsm
>Therefore, one sheet of A0 = 80 grams.
>Since A4 is 1/16th of an A0, a single sheet of standard A4 paper weighs 5 grams.
I rarely need to use a scale for postage. If I have a standard envelope (~5g) and 3 sheets of paper (15g), I know I'm at 20g total. It turns physical shipping logistics into simple integer arithmetic. The elegance of the metric system is that it makes the properties of materials discoverable through their definitions.
The person deciding to use nonstandard "GSM" as a unit instead of the proper "g/m²" needs to feel stupid...
(But arguably what whoever decided on "gsm" should have done was to just use "g", with the "per square metre" left implicit.)
"gsm", or even more so "GSM", belongs to the reign of abbrevations and put my brain on the wrong track
GSM basically only ever appears in print. If someone DOES ask "what does 120 gram mean here?" the clarification is going to be "Oh that's grams per square meter" and not "Oh that's gee es em"
I should mention GSM is also probably an americanism. I'm in the EU and out of the five packs of different kinds of art paper four are labeled in g/m2, and one has no labeled weight at all. None of them are marked in GSM as that abbreviation only works in english, while g/m2 works in all languages.
Of the four reams of paper/card I have at home, two are labelled in "gsm", one is "g.m⁻²", and one uses both "g/m²" and "gsm" in different places. Weirdly, it seems that the specialist stuff is more likely to use "gsm" than the everyday 80 g/m² A4.
mph, kph, cps, etc
0.8 megamolar = 800,000 teeth? That, uh, seems pretty wide for an interdental brush.
The symbol for molar is just the "M". "mol" denotes the Avogadro constant.
The shorthand "gsm" is a completely standard alternative in some industries.
I work in advanced composites. Different weights and weaves of technical fabrics such as carbon fiber, kevlar, fiberglass, etc. are always specified in "gsm". For example, some common fabrics would be a "Carbon Fiber 3K 200gsm Twill" or a "High Modulus 12K 380gsm Carbon Fiber Plain Weave". (the "3K" and "12K" refer to the number of carbon fiber strands in each yarn in the weave, and the "Twill" and "Plain Weave" refer to the pattern in which the yarns are woven into a fabric.)
I'm sure "gsm" came to be commonly used instead of the more scientific "g/m²" or "g/m^2" because no one is doing that kind of math about the materials, and it is a lot easier to type "gsm" vs either of the other two which require at least a Shift for the caret or getting out the superscript font attribute.
...was using a scale for postage a concern? If you're shipping things on the order of three sheets of paper, you're way below any conceivable threshold. USPS charges a flat rate on letters under 370 grams!
If you're sending 1,700 pieces of looseleaf paper in a box... just weigh the box.
https://en.wikipedia.org/wiki/Aerogram
On a related subject I just discovered that sending a letter in Denmark now costs a minimum of $4.50.
In Europe, the typical flat rate is up to 100g for standard letters. And that's 20 sheets, which is not a particularly unusual letter to send.
In the UK the limit for a letter is 100 grams:
24 by 16.5 by 0.5 cm for the standard 1st class letter. So you could send an A5 booklet made of less than 20 sheets of A4 (80 g/m^2) paper as a standard letter.
If the postage is short, our lovely privatised Post Office holds the letter and makes the recipient pay the excess.
Back on thread: Repeatedly fold an A0 sheet of paper in half. How many folds can you do? A ream (500 sheets) of 80 g/m^2 paper is about 2.5cm thick. (good when teaching geometric progressions).
Thankfully I just had a scale, but I can see this being helpful when you don't.
Do you mean in the zinc mining and Coinstar? Pennies have been a bizarre ritual for years, wherein the government made zinc worth less than its pre-minted value, distributed them to banks nationwide, banks in turn to stores, stores using them once to give meaningless amounts of money to customers, customers in turn immediately throwing them on the ground or at best eventually dumping them into a coinstar, and coinstar returned those to banks.
Nothing of value was going on there. I'd rather pay any zinc miners and coinstar drivers who have been displaced to play video games all day while still saving all those resources, fuel, and most of all, time.
Keep dimes and ramp up production of half dollars. Then we can just drop the second decimal place and standardize pricing everything in 0.1 dollar increments.
The fact that quarters are still somewhat commonly used in machines (vending machines, parking meters, laundry) is probably the biggest practical obstacle.
What I've learned from the penny retirement is that people are deeply distrustful of simple high school level statistics! Millions of people have angrily seethed that somehow stores are or will be using the penny retirement to rob them, despite knowing that most transactions have an unknowable amount of different items, and sales tax, so attempting to manipulate prices to gain a statistical advantage out of rounding would be incredibly difficult and would yield a pitiful return. Let alone how the cash transaction share is declining every year.
I’m in New Zealand and haven’t had a wallet in a decade, never using cash.
Theoretically one should carry a drivers licence when driving but it’s never come up and I have a photo of it thats worked with police before.
(I would have made a gag about a 7g replacement nickel, but you people have already used up the team "quarter" for different denomination. Although the idea of a new 40 cent coin called an "eight ball" amuses me...)
"Measure the mass of an eyelash with a DIY microbalance" by Applied Science https://youtu.be/ta7nlkI5K5g
»einen Bogen Papier zu finden, bey dem alle Formate … einander ähnlich wären. … Die kleine Seite des Rechtecks muß sich nämlich zu der großen verhalten wie 1:√2 oder wie die Seite des Quadrats zu seiner Diagonale. Die Form hat etwas angenehmes und vorzügliches vor der gewöhnlichen.«
App is about halfway down this page, https://www.fischersports.com/rc4-podium-rd-worldcup-strd/U0... under 'find your size' and is powered by https://volumental.com/
As regards metric/A* paper sizes, it seems like just a coincidence that this scheme resulted in a standard size that is useful for everyday documents, since it only works for powers of 2 and starts with the definition of 1 square meter. If a meter were 1.5x smaller or larger, then I don’t think there would be a standard size that works so well.
EDIT: Being curious about this, I did some more reading, and discovered there is a “B” series of paper sizes that maintain the same ratio relationship, but are exactly in between all the A sizes! That’s useful.
Take the length/weight relationship.
Definitionally, it'd be way more elegant for the unit of mass to be based on the unit of length directly, a cubic meter of something, but having your base unit of mass be a ton wasn't going to fly.
So they instead tried for 1/100th of the meter and landed on the gram, but it turns out they misjudged and now your standard unit of weight is the prefixed kilogram instead, because everyone used kilograms instead.
Which is to say, if you didn't get a pretty good paper size out of the definition used for A0, someone would have found a different definition which did produce a pretty good paper size, and then declare it was the only natural one.
See also C series. Thankfully largely a moot point now.
Off-topic but as a non-native English speaker, TIL what svelte means lol. I often get exposure of new words first from a product name. Same happened with Chrome.
Let me introduce to you: the IKEA paper tape measure, folded neatly in your wallet.
(read the article)
29.7 is close to 30. So why not use A4 sheets to install kitchen cabinets? A friend of mine advised me to buy a laser level. A tiny level was quite enough. A laser meter is nice though although I don't understand why it's inaccurate sometimes. Maybe it depends on the surface matter/paint.
0: https://www.youtube.com/watch?v=pUF5esTscZI
edit: fat-fingered CPG, thanks @ProllyInfamous
----
My favorite CGP Grey video is Metric Paper..., which explores the vast (but limited) world we live in, from plancs to observable universe.
[•] <https://www.youtube.com/watch?v=pUF5esTscZI>
Before generative AI videos, this had been what I considered "the most psychedelic experience one can have without doing drugs." It's still a trip...
Just quoting the author here, haha.
https://en.wikipedia.org/wiki/International_standard_paper_s...
Edit: while going through the article again, I noticed that's a brief mention of the ISO standard, which I missed in the first round.
I’ve started to determine the right package of paper towels to purchase according to the cents per square meter value. You can discern the quality of a deal at the grocery by referring to the ‘cents per X’ market located on price tag next to the marked price.
I’m beginning to turn sour on the ‘2 Jumbo-Mega-Rolls are the equivalent of 8 Super rolls’ scheme that’s en vogue. Are there retractable roll holders to accommodate for all of this?
It doesn’t help that many of these packages are priced and then marked down in ways to entice the buyer toward purchasing them instead of more reasonably priced and proportioned ones.
It is complicated area. Not to even get to loo roll. Where I noticed that the ecological one I bought feels quality wise inferior to normal one. And this is premium type of stuff. So it sits between the premium and cheap, but more on premium end.
I never understood the US paper size system while living there (or since...!), don't get me started with feet and inches and 16'ths etc - ISO, metric and base10 is just so much more logical and easy to use...
Heck, I’m pretty sure you could get a sheaf of it at any number of office supply stores right now if you wanted.
Unless you have mobile paper shops. Could be handy, but seems a bit niche.
Or you can buy a ream of legal-size and have a printshop slice it down (which is how I got ahold of B4 or B5 IIRC).
I buy A4 notebooks all the time. I use fountain pens, so many of the notebooks and even loose paper with the proper sizing (coating, that is) usually come in EU sizes. Tomoe River... Clairfontaine... etc.
It's a good exercise in thinking, dhy that is so.
Lol
European: "Yes, but not your everyday sources."
1190mm (A0 height) / 841mm (A0 width) ⩰ √2
11" (US letter height) / 8.5" (US letter width) = 1.29411 ...
Countries using the Metric system: 192
Countries using the Imperial system: 3 (U.S., Liberia, Myanmar)
The U.S. rejection of the Metric system can be traced to Thomas Jefferson, who declared it "Too French."
I remember when I first got into metal work and wanted to get some tapping drills.
There are a plethora of standards when you start looking into it. For what I make though if I use metric I really only need one, ISO Coarse.
Metric is just well thought out and easier.
Screw sizes and drill sizes should have been sized by a ratio, like resistor values. But that would have been a pain for manual machining.
Domestic drill sets don't seem to be designed for tapping holes but if you stick to M3, M6 and M10 the tapping sizes do correspond with the 2.5, 5 and 8.5mm drills[1].
I guess if it was based on a ratio system you would need special tapping drills for all of them.
e.g. M4 needs a special 3.3mm tapping drill already.
1. According to my trusty Zeus tables.
When I spread my index finger and middle finger, not entirely as far as they can go, but rather far, that's 10 centimetres.
Thumb to pinky is 22 centimetres. These two are often precise enough for me.
You could have memorized the length of a cheapo Bic pen if that is common in your area; Or a Parker or a Monte-Blanc if you carry one of those.
All recent iPhones (regular models since `03) have a width of 71.5mm. Remember that, and as long as someone near you has an iPhone, you are good to go using it as a ruler. (And people will definitely be, um, impressed).
We have in my kitchen several brands of small forks, all are 19.2mm (just checked. The large forks have a range of sizes). Next time I need to measure something I could just request a fork...
urbandw311er•1d ago
sunrunner•1d ago
Although I still haven't figured out the best way to do that in reverse (when someone wants a specific measurement and I cut the string from that number), though I was considering a scheme where I start with strings of known length up-front then repeatedly cut successive halves until I converge on the desired number, accounting for cut accuracy and require precision.
madcaptenor•1d ago
saalweachter•1d ago
When working on a project where you need a bunch of things to be the same, you take a stick and mark on it at various points the dimensions you're using -- when working on a house, it might be things like the heights of outlet boxes and switches, the width and height of rough opening for doors, the height of window sills, etc etc.
Then, you just use the stick as the reference, using the marking for outlets to position all of the outlets instead of measuring the height of the floor in inches or millimeters or cubits or whatever each time. It's kind of like a measuring jig.
("Measure once, cut twice" is a superior methodology which has been unfairly maligned for generations.)
tonyarkles•1d ago
It feels really imprecise the first time you set the fence on a table saw based on a marking on a stick instead of a precise specific value but the results are hard to argue with.
saalweachter•1d ago
Sure, check your measurements to be sure they're correct, but the more times you can cut based on the same measurement, the less measurement error can creep in.
tonyarkles•23h ago
A similar strategy I've used when I've known that there was going to be cuts that I couldn't sequence like that is to cut "as built" story sticks with scrap dimensional lumber and write what they are right on the board.
Dilettante_•23h ago
madcaptenor•21h ago
woliveirajr•1d ago
[0] https://www.amazon.com/Measure-iBayam-Measuring-Measurement-...
mhb•1d ago
testing22321•1d ago
layer8•23h ago
Lio•21h ago
That works but with a piece of paper you can tell the time too, so long as you get a nice man to write it down for you[1]. ;)
1. And now the confusion of having to explain the Goon Show: https://www.youtube.com/watch?v=rLQhQSiDR-k
MinimalAction•20h ago