Nice! The author touches on the area properties and here's the most practical life hack derived from the standard I personally use. It uses the relationship between size and mass.
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.
Don't tell the current administration that there's something so un-American about the currency: they will insist on fixing it, and probably retire Jefferson as well.
Fun fact: While the US spent more than 3 cents for every penny minted and distributed, it spends about 14 cents for every nickel minted and distributed!
When they decided to stop minting pennies I think they should have gotten rid of nickels and (I know this will be controversial) quarters as well!
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.
This may be the most practical go-forward plan. The Euro's .20 coins are also attractive too. But you're correct that quarters, as the smallest common currency that you can plausibly buy something with just a couple of them, are just everywhere, from laundry to car washes, so the pain in retiring them would be widely felt.
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.
We need to keep the physical dimensions and material properties of the quarter, but why not change the face value? Demote them to 20 cents, or even better, make them 50 cents because the real half dollar coin is obnoxiously huge and impractical.
What of the economic impact of doubling the value of all quarters? Eh, it'll probably be fine. We'll just write it off as an AI datacenter loan somehow
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.
I, for one, look forward to the new 5oz "Donald Trump Freedom Nickel". Probably resulting from a deal he did with the Big Trousers lobby groups to wear out coin pockets faster.
(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...)
I'm not sure I agree. "GSM" is three syllables, versus four for "grammes per square metre". You can write it correctly using only characters everyone knows how to type quickly on their keyboard, versus either finding a way to get that superscript ² or else typing something like g/m^2 which is uglier and longer. And you can use it comfortably even if you are a complete mathematical ignoramus (you just need to know things like "larger numbers mean heavier paper" and "cheap printer paper is about 80gsm" and so forth) without the risk of turning g/m² into the nonsensical g/m2 or something.
(But arguably what whoever decided on "gsm" should have done was to just use "g", with the "per square metre" left implicit.)
Roughly no one already says GSM. When talking about paper you'll hear people say things like "That's a sheet of 120 gram"
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.
In the UK, "gee es em" was the usual term I heard at the local paper merchants when I was a regular customer in the late 90s - early 2000s.
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.
"The person deciding to use nonstandard "GSM" as a unit instead of the proper "g/m²" needs to feel stupid..." ---> This is the sort of HN comment that I can't figure out if it's serious or a joke. I can read it in different voices and come to opposite conclusions haha
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.
Interestingly, sail cloth (for sail boat sails) is measured in ounces per square yard, and is just referred to by the weight with the square yard assumed - like "8oz Nylon mainsail" or "4oz ripstop spinnaker". (Or at least it used to be, my expertise here is more than 30 years out of date now.)
Curious what you're doing that "kilograms per hour" might get used by normal people in everyday conversation. Fast food restaurant or a weight loss clinic?
Agreed but we do have to interact with them. I once tried to sell a car with 140 Mm and got nowhere. I then changed the add to 140_000 km and got a lot more interest.
Oh nice, that is a neat trick! One small nitpick (that makes no difference): The side lengths of the ISO Ax formats are rounded to the next mm, so actually the A0-format has an area of 0.999949m^2
that reminds me of an old joke: how doe the postal services make their profit? I don't get it. - Ah, that's easy. How much wieght may letters have? - 20g - And how much weight do the average letters have? - About 6g. - See? That's their profit
> 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.
...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.
German postage for letters is under 20g, under 50g and under 500g so I had this issue a few times so far when sending a few letters a day over a few weeks. You can see it here for international letters for example: https://www.deutschepost.de/en/b/briefe-ins-ausland.html
Thankfully I just had a scale, but I can see this being helpful when you don't.
But 20 sheets do not fit in a regular DL or C5 envelope so you already have an hint that you may check the limits, you usually send them in a reinforced C4 enveloppe.
And as that link eventually shows there are limits on the dimensions as well. I sometimes think a simple table might be better than these interactive pages, but I suppose it has to work on a phone.
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).
As a European living in North America I developed a weird cognitive dissonance. When I'm in North America the regular printer page (US Letter) seems too squat. When I'm in Europe the A4 page looks too svelte. I now need an in-between format for it to look "right".
> When I'm in Europe the A4 page looks too svelte.
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.
I happened to be looking at ski boot fitting this morning and came across a web app from fischersports that allows you to measure your feet using your phones camera. Surprise surprise it uses a sheet of A4 paper.
Fun article. I liked the bit about how the size of A0 can be uniquely determined from abstract constraints. But I'm not convinced that the "Measuring Stuff" section involves anything more than memorising the exact dimensions of A4. I don't see how it applies the stuff about preserved ratios.
25. Of October 1786: Lichtenberg suggested his friend Beckmann a paper format in the aspect ration 1/√2.
»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.«
Here’s a better tip to measure things without a proper measuring device: spread out your hand on a table and measure the distance between your pinky and thumb. Remember that. Now when you need to measure something just measure it in number of pinky-thumb-stretches. I can quickly get the dimensions to +/- an inch by doing a few quick walks with my hand.
It is hand to remember a few finger/knuckles/elbow/shoulder combinations for common measures. One of your phalanges should be ~1 inch, for example, and one of your finger nails is probably ~1 cm wide.
There's a reason that the English system of measurement had things like "hand" and "foot" - because when you're not measuring things exactly, close enough and commonly available is fine.
For small screws, in the millimeter range, the jump between metric sizes is too big. So, in addition to M1, M2, M3, M4, M5, etc. standard metric screws include M1.4, M1.6. M1.8, M2.5, and M3.5 (rare) to fill in the gaps.
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.
I am glad I came back and reread this -- I misunderstood it as thumb to middle finger at first, and thought it incredibly tiny.
Index to middle finger is 15cm for me, without stretching uncomfortably, and thumb to little finger ("pinky") is 26cm. Outside to outside of the fingers.
(For comparison I am a 1.88m -- 6'2" -- male.)
This is why I like large smartphones. The original tiny ones felt like using cocktail sticks as chopsticks to me: they were tiny and toylike and required superhuman precision.
6.5" phones are just about usable, especially with swipe-typing. Almost all Blackberry models were unusably small and cramped for me, but the Passport was OK.
My partner (an architect) does something similar, plus - when she holds her arm out straight - the distance from the tips of her fingers to the opposite shoulder blade is almost exactly a meter.
As an American I have done this with 8.5 x 11 "letter" paper. I wonder if there's some way one can take advantage of the special properties of A[n] paper.
1000% yes! An 8.5x11" paper is effectively a 12" ruler accurate to 2 decimal places.
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.
As a long time European I never thought I’d come to see the sense of American ways, but having lived here now for a couple of years, it actually is easier for it to just be straight up 8.5 x 11 rather that a ratio that includes a square root.
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.
Many, many people want to double or halve documents.
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.
Sorry, I should have specified "and have it look perfect".
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.
That's not a difference between ANSI and ISO paper sizes.
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.)
So, regarding books, why do you think the methods of printing books varies based on the size of the printing sheets?
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.
I've been working with paper sizes a lot for the last year, and I've rarely thought about the square root of two ratio and when I've, it has been just to amuse myself. However, knowing that to get an A5 piece of paper I just need to cut/fold in half an A4, and that I can get to A3 and A2 by adding A4s, has been really useful. If I were in USA, didn't have that, and instead would have to install yet another new size system in my head[^1], I would despair.
What bothers me mostly about American papersizes (I’m also a European immigrant) is that the ratio is not consistent between sizes. So if I design a poster, but want a couple of letter sized printouts for some reason, I have to create a whole new design, rather then just shrink everything down. Otherwise the margins get all wonky.
One nice thing with Letter size is you can fit 80 columns of 10 dpi text with standard LaserJet margins. With A4 you have to squeeze the characters together slightly to make that fit.
A[n] sizes are useful when enlarging or shrinking documents. Enlarge or shrink by muliples of sqrt(2) and there's always a fitting paper size available. Or you can put two A5s together on an A4, or two A4s on an A3.
> I wonder if there's some way one can take advantage of the special properties of A[n] paper.
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.
As a consumer I used to use it all the time, though it matters a lot less these days. Two A4 pages at 50% zoom (A5) fit on one A4. You could cut your printing cost for drafts in half by doing that, back when we had to actually print to check the layout. Same went for posters etc, and since the aspect ratio was preserved it was really handy to preview at home on A4 sheet before taking it to the print shop.
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".
Sizing errors are essentially unheard of, and I've never seen anyone having any trouble with joining or folding ISO paper to go one size up/down. It's a completely normal operation, which people working in printing and publishing will routinely do without a second thought.
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.
As the other commenter said, alignment issues have never been a problem.
If you're manually aligning the sheets on the photocopier bed maybe, but the edges are set up for that so it's never been an issue for me. However every photocopier I've used that was made since the late 90s lets you do the sheets individually so you can use the copier bed to align each one.
Because the ability to scale like this is so ubiquitous we're just all used to doing it.
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.
With paper towel I have been thinking that the area might not be important, but the number of sheets would be. As long as they do not get too small. And then there is also the quality and if they are half or full. For some uses you just want the full.
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.
Although that doesn’t speak to the actual quality of the individual layers of paper. I’m not sure if weight is useful especially when manufacturers are already putting their thumb on the scale in other ways with the ‘2 Jumbo-Mega-Rolls are the equivalent of 8 Super rolls’ scheme that I initially referred to.
If all weight can tell me is that 2-Jumbo-Mega Rolls weigh the same as 8 Super rolls am I any better informed?
This is why I’m pretty content with using the price in cents per square foot as a baseline. In general it’s a useful metric when shopping elsewhere at the grocery store too.
The worst is that the assumption that the greater quantity is cheaper per unit, but for some reason that's not always true so you have to sit there and do the math in order to get the best deal.
I've participated in (and now have been a ref for) a robotics competition, First Lego League, a couple of times. The robots can have a height of up to 30.5cm (12"), and that's usually quickly checked before each round.
Since there's pretty much always some A4 paper lying around near you, probably a copy of the rules, in most situations we just hold up a sheet (rolled up if you're feeling fancy) next to the robot. Much quicker than finding the ruler that's probably in use (or misplaced) somewhere else :D
Maths Youtuber Noel Friedrich recently made a video about A4 paper[0]. It turns out that since the ISO specification rounds the side lengths down to whole millimeters, with compounding errors, more than 2^10 A10s (smallest paper size in the standard) fit into one A0 (largest size in the standard).
Ha - I have made so many measurements using an A4 with great accuracy that this monitor-story might as well have been me :-)
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...
While this is nice, it is not inherently related to an A4 paper.
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...
I use my phone when I want to measure stuff. Not an app, just the physical phone as a ruler. Almost always the dimensions of whatever phone I've got is published on the internet. It's a quick hack and better than carrying around A4 papers ;)
Pythagoras would appreciate her usage of his theorem, but I'd have just laid my papers diagonally across the screen to measure it directly without computing any square roots. Since I'm a yank, 11 + 11 + 5.5 would do quite nicely.
At one point on an international project I had to fly a box of UK A4 to the USA in my luggage so the Americans could check their software could cope with the different size. It did, but lugging it around was a pain - paper is heavy!
I don’t know what specialty stores you’re talking about but A4 is readily available at most stationary stores, or anything related to letter writing, pens, or paper. I got the A5 notebook I’m currently using at Barnes and Noble, they also have A4.
Heck, I’m pretty sure you could get a sheaf of it at any number of office supply stores right now if you wanted.
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.
Kodak used to have an industrial printer partnership with Heidelberg. They would test their printers with pallet loads of A4. Most I've ever seen in the US.
I had the reverse, we had to get a ream of US Letter and corresponding envelopes sent over so we could ensure the layouts printed properly. Also some chequ… “checks” which were fascinating.
An interesting question, but I think it would be very hard to do it accurately. Also, some of the reports the needed to print during testing were looong.
Yeah, I’ve used a sheet of paper as a ruler too...
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.
The creators of metric weren't above buggering it to fit human scale needs.
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.
I don't think anybody loses sleep over the kilogram issue because, well, it's metric after all. A kilogram is exactly 1000 grams, so the gram is just as perfectly well defined. Nothing would really change if they were to promote the gram to be the standard unit of mass (not weight!) someday.
Elegant, sure, but... fold a sheet of US Letter (8.5 x 11.0 inches) in half, and you're on your way to a pirate hat. Fold and pull it several more times, and you have a boat.
Some Moleskine cahier notebooks are wrapped in a paper sleeve that has a ruler printed on the back. Inches on one edge; centimetres on the other (a slight improvement for non-American users over Field Notes notebooks, with a ruler on the inside back cover that’s inches only - also the sleeve is rather longer, 28cm in fact).
21cm is close to 20 which means A5 has a side close to 10.
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.
Sqrt(2) being halfway between 1 and 2 multiplicatively, leads to interesting stuff. For example consider two integers A and B. They have a dual in the pair A+B and A-B. Well, not quite. You need to scale them down by 1/sqrt(2). If you do that to the duals, you get the originals again.
As the ratio used is a rational approximation of an irrational, I would guess that the ratio-preserving feature breaks down well before you get to atomic sizes, though I have neither proved that to be so nor figured out how to calculate the divergence.
If you have a Pro or Pro Max model of iPhone from the last several years, it has a LiDAR that allows the pre-installed Measure app to measure lengths/heights, etc., using the camera. Several higher end Android phones may also have the same.
> "Hold on. I think I hear another heckle. What is that? There are mobile phone apps that can measure things now? Really? Right. Security. Where's security?"
Hint: The aspect ratio sqrt(2) should be quite convenient for foldable phones. Current ones seem to be more or less square if unfolded - what use case is that good for?
I read the article, but is there any evidence suggesting the Apple measuring app is insecure? It only collects data not linked to you (usage data and diagnostics) and is using the same privacy policy as the Apple camera app, which pretty much every iPhone user is trusting already.
Trying not to be too negative but this is quite a long blog post for what effectively just comes down to using a piece of paper to measure something, which I imagine lots of us have done in a pinch. Also, nit: one of the calculations on paper size seems duplicated due to a typo.
Personally I make sure to always carry around a string and some scissors, so any time I need an arbitrary measurement I can just cut the string to the length of the thing I want to measure (making sure to label it in case of multiple required measurements), then measure the cut string later. Simple.
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.
Maybe you could start off with a long string and then mark off its midpoint, the midpoints of the halves, and so on. Then you wouldn't have to cut a new string every time you want to measure something.
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.)
This works fantastic for building furniture as well, where the absolute dimension doesn’t matter as much as all of the pieces having matching dimensions. A cabinet with drawers, for example. The story stick captures the spacing between the drawers, the width of the drawer, the slightly smaller height of the drawer face, etc.
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.
With carpentry in particular, it is extremely powerful to make multiple cuts at the same time -- set a fence once and then cut everything that needs to match at the same time, or stack multiple pieces together, or cut a board to length before ripping it into several pieces that need identical lengths.
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.
Was going to mention that too. 100% agree. If I mess up and end up needing to make matching cuts later on, I'll often set the fence using one of the existing pieces too instead of trying to re-measure. The story stick works great but lining up the teeth on the blade with the cut edge of an existing piece works fabulously well.
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.
What, and use the same thing to measure stuff anytime you measure something? Like that's ever gonna catch on! Next you're gonna tell me to use my lower arm as a measuring stick!
The span from my thumb to my pinky in a “measuring position” is 20 cm (and is easily repeated by moving the thumb to the pinky and then stretching out the pinky again). The length of my “thumbs up” hand is 16 cm. The width of my fist is 10 cm. The length of my pinky is 6 cm. The width of my thumb is 2 cm. This allows me to estimate distances between ~2 m and 2 cm pretty well. Knowing your foot/shoe length also comes handy sometimes.
Nice! The author touches on the area properties and here's the most practical life hack derived from the standard I personally use. It uses the relationship between size and mass.
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 5 grams per sheet of common printer paper has certainly proven handy once or twice in some of my interactions in the informal economy.
Same for the US 5 cent coin. Defined mass of 5 grams.
Don't tell the current administration that there's something so un-American about the currency: they will insist on fixing it, and probably retire Jefferson as well.
Fun fact: While the US spent more than 3 cents for every penny minted and distributed, it spends about 14 cents for every nickel minted and distributed!
When they decided to stop minting pennies I think they should have gotten rid of nickels and (I know this will be controversial) quarters as well!
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.
This may be the most practical go-forward plan. The Euro's .20 coins are also attractive too. But you're correct that quarters, as the smallest common currency that you can plausibly buy something with just a couple of them, are just everywhere, from laundry to car washes, so the pain in retiring them would be widely felt.
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.
We need to keep the physical dimensions and material properties of the quarter, but why not change the face value? Demote them to 20 cents, or even better, make them 50 cents because the real half dollar coin is obnoxiously huge and impractical.
What of the economic impact of doubling the value of all quarters? Eh, it'll probably be fine. We'll just write it off as an AI datacenter loan somehow
I would have gotten rid of nickels and dimes; then everything is priced in 1/4 dollars.
Which is pennies compared to the amount of economic activity that those pennies facilitated.
> activity that those pennies facilitated
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.
I mean really, everything smaller than a quarter should go.
Erasing small coins will be an interesting race between inflation and electronic payments.
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, for one, look forward to the new 5oz "Donald Trump Freedom Nickel". Probably resulting from a deal he did with the Big Trousers lobby groups to wear out coin pockets faster.
(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...)
And $20 in dimes or quarters is 1 lb. US silver coins are 0.2268 grams per cent.
Paper's uniform mass per area makes it useful calibrating very tiny scales. 1mm² of 80 gsm paper will weigh about 80 micrograms.
"Measure the mass of an eyelash with a DIY microbalance" by Applied Science https://youtu.be/ta7nlkI5K5g
TIL GSM is just g/sq m. Like duh, feel so stupid xD
It's not you who should feel stupid.
The person deciding to use nonstandard "GSM" as a unit instead of the proper "g/m²" needs to feel stupid...
I'm not sure I agree. "GSM" is three syllables, versus four for "grammes per square metre". You can write it correctly using only characters everyone knows how to type quickly on their keyboard, versus either finding a way to get that superscript ² or else typing something like g/m^2 which is uglier and longer. And you can use it comfortably even if you are a complete mathematical ignoramus (you just need to know things like "larger numbers mean heavier paper" and "cheap printer paper is about 80gsm" and so forth) without the risk of turning g/m² into the nonsensical g/m2 or something.
(But arguably what whoever decided on "gsm" should have done was to just use "g", with the "per square metre" left implicit.)
Roughly no one already says GSM. When talking about paper you'll hear people say things like "That's a sheet of 120 gram"
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.
In the UK, "gee es em" was the usual term I heard at the local paper merchants when I was a regular customer in the late 90s - early 2000s.
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.
I guess the fact that over here GSM was also the term for a mobile phone for the longest time has affected things some.
I beg to differ. You can totally get away with g/m2 which is not hard to type and crucially has a / to hint you what it could be about
"gsm", or even more so "GSM", belongs to the reign of abbrevations and put my brain on the wrong track
"The person deciding to use nonstandard "GSM" as a unit instead of the proper "g/m²" needs to feel stupid..." ---> This is the sort of HN comment that I can't figure out if it's serious or a joke. I can read it in different voices and come to opposite conclusions haha
While we're at it, mph and the abomination that is "kph" (= km/h) even more so need to die in a fire.
Some cursory search suggests "gsm" for grammature is confined to the US, everyone else uses g/m² or just g.
It's gsm in the UK too
You mean gm⁻² ?
Well, yes. I was just too lazy to find the superscript minus ;)
Ummm, not really, No.
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.
Interestingly, sail cloth (for sail boat sails) is measured in ounces per square yard, and is just referred to by the weight with the square yard assumed - like "8oz Nylon mainsail" or "4oz ripstop spinnaker". (Or at least it used to be, my expertise here is more than 30 years out of date now.)
> The person deciding to use nonstandard "GSM" as a unit instead of the proper "g/m²" needs to feel stupid...
mph, kph, cps, etc
I most definitely grew up with km/h, not kph. "k" is not an acceptable way to abbreviate kilometer in a world where kilograms are used.
Curious what you're doing that "kilograms per hour" might get used by normal people in everyday conversation. Fast food restaurant or a weight loss clinic?
The whole point of SI units is to not live in a world of uncertainty, ad hoc terminology, and name collisions.
Yeah, the people insisting on writing those are on the wrong.
Agreed but we do have to interact with them. I once tried to sell a car with 140 Mm and got nowhere. I then changed the add to 140_000 km and got a lot more interest.
My interdental brushes claim that the wire is 0.8 megamolar wide, which is not a normal measure of width.
I wonder if the international society of dentists keeps a standard molar in a safe somewhere
It is probably an indication that they should fix their caps lock keys, however. Like the guys who sells bottles with volumes in ML.
That would be 4.82x10²⁹ somethings wide.
> My interdental brushes claim that the wire is 0.8 megamolar wide, which is not a normal measure of width.
0.8 megamolar = 800,000 teeth? That, uh, seems pretty wide for an interdental brush.
0.8 Mmol?
0.8 MM
The symbol for molar is just the "M". "mol" denotes the Avogadro constant.
Oh nice, that is a neat trick! One small nitpick (that makes no difference): The side lengths of the ISO Ax formats are rounded to the next mm, so actually the A0-format has an area of 0.999949m^2
Not to the next, to the nearest, otherwise it would have to be slightly larger than 1m^2.
that reminds me of an old joke: how doe the postal services make their profit? I don't get it. - Ah, that's easy. How much wieght may letters have? - 20g - And how much weight do the average letters have? - About 6g. - See? That's their profit
I really don't get it.
It's technically a 300% margin because they are charging you for 20g but only shipping 6g.
> 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.
...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.
German postage for letters is under 20g, under 50g and under 500g so I had this issue a few times so far when sending a few letters a day over a few weeks. You can see it here for international letters for example: https://www.deutschepost.de/en/b/briefe-ins-ausland.html
Thankfully I just had a scale, but I can see this being helpful when you don't.
Given that we are talking about A4 papers and grams, I'd bet this wasn't in the US.
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.
But 20 sheets do not fit in a regular DL or C5 envelope so you already have an hint that you may check the limits, you usually send them in a reinforced C4 enveloppe.
French "La Poste" sets the first threashold at 20 g.
You will be using Aerograms soon.
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.
>USPS charges a flat rate on letters under 370 grams!
In the UK the limit for a letter is 100 grams:
https://www.royalmail.com/sending/uk/1st-class
And as that link eventually shows there are limits on the dimensions as well. I sometimes think a simple table might be better than these interactive pages, but I suppose it has to work on a phone.
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).
In Sweden, the lowest postage (one stamp, 22 SEK or around $2) is for max 50 grams.
A first class forever stamp only covers 1oz (28g).
CGP Grey has a video [0] that goes into some, let's just say deeper, detail into metric paper that is well worth a watch if you haven't seen it.
0: https://www.youtube.com/watch?v=pUF5esTscZI
edit: fat-fingered CPG, thanks @ProllyInfamous
You beat me in posting this (I searched for "CGP," first — you mispelled so I didn't see your comment).
----
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...
As a European living in North America I developed a weird cognitive dissonance. When I'm in North America the regular printer page (US Letter) seems too squat. When I'm in Europe the A4 page looks too svelte. I now need an in-between format for it to look "right".
> When I'm in Europe the A4 page looks too svelte.
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.
B5
Assuming "squat" and "svelte" refer to the aspect ratio, isn't B5 going to look just as "svelte" as A4?
B series paper sizes is a thing I knew but wish I didn't.
See also C series. Thankfully largely a moot point now.
Also sqrt(2) isn't the golden number. Not far from it but still...
The golden ratio makes for even less balanced paper than sqrt(2)
I happened to be looking at ski boot fitting this morning and came across a web app from fischersports that allows you to measure your feet using your phones camera. Surprise surprise it uses a sheet of A4 paper.
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/
Fun article. I liked the bit about how the size of A0 can be uniquely determined from abstract constraints. But I'm not convinced that the "Measuring Stuff" section involves anything more than memorising the exact dimensions of A4. I don't see how it applies the stuff about preserved ratios.
Nitpick: typo in the dimensions for A3.
The article declines to mention how precise paper is. The corners are very, very square and the lengths are very, very precise.
Better than an average square, better than an average ruler.
On one hand, you could do the measuring section with any standardized rectangle. On the other hand, any excuse to talk about metric paper
Letter paper, credit card, banknote, business card, etc.
25. Of October 1786: Lichtenberg suggested his friend Beckmann a paper format in the aspect ration 1/√2.
»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.«
Here’s a better tip to measure things without a proper measuring device: spread out your hand on a table and measure the distance between your pinky and thumb. Remember that. Now when you need to measure something just measure it in number of pinky-thumb-stretches. I can quickly get the dimensions to +/- an inch by doing a few quick walks with my hand.
It is hand to remember a few finger/knuckles/elbow/shoulder combinations for common measures. One of your phalanges should be ~1 inch, for example, and one of your finger nails is probably ~1 cm wide.
There's a reason that the English system of measurement had things like "hand" and "foot" - because when you're not measuring things exactly, close enough and commonly available is fine.
Only, I think, a foot is actually a half a cubit (length from elbow to fingertip). So, sort of a misnomer, rounded to the nearest body part.
Or be like the mythbusters guy and get a ruler tattooed on your arm!
Metric is beautiful.
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.
For small screws, in the millimeter range, the jump between metric sizes is too big. So, in addition to M1, M2, M3, M4, M5, etc. standard metric screws include M1.4, M1.6. M1.8, M2.5, and M3.5 (rare) to fill in the gaps.
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.
Yep, as it is some sizes are easier to work with.
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.
I use my fingers:
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.
I am glad I came back and reread this -- I misunderstood it as thumb to middle finger at first, and thought it incredibly tiny.
Index to middle finger is 15cm for me, without stretching uncomfortably, and thumb to little finger ("pinky") is 26cm. Outside to outside of the fingers.
(For comparison I am a 1.88m -- 6'2" -- male.)
This is why I like large smartphones. The original tiny ones felt like using cocktail sticks as chopsticks to me: they were tiny and toylike and required superhuman precision.
6.5" phones are just about usable, especially with swipe-typing. Almost all Blackberry models were unusably small and cramped for me, but the Passport was OK.
My partner (an architect) does something similar, plus - when she holds her arm out straight - the distance from the tips of her fingers to the opposite shoulder blade is almost exactly a meter.
As an American I have done this with 8.5 x 11 "letter" paper. I wonder if there's some way one can take advantage of the special properties of A[n] paper.
1000% yes! An 8.5x11" paper is effectively a 12" ruler accurate to 2 decimal places.
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.
As a long time European I never thought I’d come to see the sense of American ways, but having lived here now for a couple of years, it actually is easier for it to just be straight up 8.5 x 11 rather that a ratio that includes a square root.
It's an interesting tiny trade-off.
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.
Many, many people want to double or halve documents.
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.
Sorry, I should have specified "and have it look perfect".
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.
You are wildly wrong in your assumption that the folding property has low value.
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.
That's not a difference between ANSI and ISO paper sizes.
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.)
Oh, you're talking about books, not sheets? My reply is probably all wrong, sorry.
So, regarding books, why do you think the methods of printing books varies based on the size of the printing sheets?
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.
I've been working with paper sizes a lot for the last year, and I've rarely thought about the square root of two ratio and when I've, it has been just to amuse myself. However, knowing that to get an A5 piece of paper I just need to cut/fold in half an A4, and that I can get to A3 and A2 by adding A4s, has been really useful. If I were in USA, didn't have that, and instead would have to install yet another new size system in my head[^1], I would despair.
[^1]: This is fun! https://papersizes.io/us/
What bothers me mostly about American papersizes (I’m also a European immigrant) is that the ratio is not consistent between sizes. So if I design a poster, but want a couple of letter sized printouts for some reason, I have to create a whole new design, rather then just shrink everything down. Otherwise the margins get all wonky.
One nice thing with Letter size is you can fit 80 columns of 10 dpi text with standard LaserJet margins. With A4 you have to squeeze the characters together slightly to make that fit.
A[n] sizes are useful when enlarging or shrinking documents. Enlarge or shrink by muliples of sqrt(2) and there's always a fitting paper size available. Or you can put two A5s together on an A4, or two A4s on an A3.
> I wonder if there's some way one can take advantage of the special properties of A[n] paper.
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.
As a consumer I used to use it all the time, though it matters a lot less these days. Two A4 pages at 50% zoom (A5) fit on one A4. You could cut your printing cost for drafts in half by doing that, back when we had to actually print to check the layout. Same went for posters etc, and since the aspect ratio was preserved it was really handy to preview at home on A4 sheet before taking it to the print shop.
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.
> Two A4 pages at 50% zoom (A5) fit on one A4.
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".
Sizing errors are essentially unheard of, and I've never seen anyone having any trouble with joining or folding ISO paper to go one size up/down. It's a completely normal operation, which people working in printing and publishing will routinely do without a second thought.
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.
As the other commenter said, alignment issues have never been a problem.
If you're manually aligning the sheets on the photocopier bed maybe, but the edges are set up for that so it's never been an issue for me. However every photocopier I've used that was made since the late 90s lets you do the sheets individually so you can use the copier bed to align each one.
Because the ability to scale like this is so ubiquitous we're just all used to doing it.
Paper Towel stories:
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.
With paper towel I have been thinking that the area might not be important, but the number of sheets would be. As long as they do not get too small. And then there is also the quality and if they are half or full. For some uses you just want the full.
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.
As mentioned in a sibling comment, weight might need to be accounted for too: thicker paper is more absorbant, but not linearly so.
So really, how absorbant the paper is should be the gold standard, so let's ask manufacturers to put that on the packaging?
Manufacturers already indicate to the thickness of their paper with ply count: <https://blog.whogivesacrap.org/home/difference-ply-toilet-pa...>.
Although that doesn’t speak to the actual quality of the individual layers of paper. I’m not sure if weight is useful especially when manufacturers are already putting their thumb on the scale in other ways with the ‘2 Jumbo-Mega-Rolls are the equivalent of 8 Super rolls’ scheme that I initially referred to.
If all weight can tell me is that 2-Jumbo-Mega Rolls weigh the same as 8 Super rolls am I any better informed?
This is why I’m pretty content with using the price in cents per square foot as a baseline. In general it’s a useful metric when shopping elsewhere at the grocery store too.
The worst is that the assumption that the greater quantity is cheaper per unit, but for some reason that's not always true so you have to sit there and do the math in order to get the best deal.
Since not all paper is of the same thickness, shouldn't you compare "weight per price"?
I've participated in (and now have been a ref for) a robotics competition, First Lego League, a couple of times. The robots can have a height of up to 30.5cm (12"), and that's usually quickly checked before each round.
Since there's pretty much always some A4 paper lying around near you, probably a copy of the rules, in most situations we just hold up a sheet (rolled up if you're feeling fancy) next to the robot. Much quicker than finding the ruler that's probably in use (or misplaced) somewhere else :D
Maths Youtuber Noel Friedrich recently made a video about A4 paper[0]. It turns out that since the ISO specification rounds the side lengths down to whole millimeters, with compounding errors, more than 2^10 A10s (smallest paper size in the standard) fit into one A0 (largest size in the standard).
[0] https://www.youtube.com/watch?v=zDKBCIMkDbw
Ha - I have made so many measurements using an A4 with great accuracy that this monitor-story might as well have been me :-)
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...
While this is nice, it is not inherently related to an A4 paper.
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...
I use my phone when I want to measure stuff. Not an app, just the physical phone as a ruler. Almost always the dimensions of whatever phone I've got is published on the internet. It's a quick hack and better than carrying around A4 papers ;)
Pythagoras would appreciate her usage of his theorem, but I'd have just laid my papers diagonally across the screen to measure it directly without computing any square roots. Since I'm a yank, 11 + 11 + 5.5 would do quite nicely.
At one point on an international project I had to fly a box of UK A4 to the USA in my luggage so the Americans could check their software could cope with the different size. It did, but lugging it around was a pain - paper is heavy!
I wish we could buy A4 paper in North America! I find it surprising it's not available even in specialty stores. The rest of the world uses it!
You may need to look for 8.27" x 11.69" - https://www.staples.com/hammermill-copy-plus-8-27-x-11-69-co...
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 don’t know what specialty stores you’re talking about but A4 is readily available at most stationary stores, or anything related to letter writing, pens, or paper. I got the A5 notebook I’m currently using at Barnes and Noble, they also have A4.
Heck, I’m pretty sure you could get a sheaf of it at any number of office supply stores right now if you wanted.
* stationery :-)
Unless you have mobile paper shops. Could be handy, but seems a bit niche.
Well I've never seen one move!
For printers?
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.
Kodak used to have an industrial printer partnership with Heidelberg. They would test their printers with pallet loads of A4. Most I've ever seen in the US.
Yo do know all the jokes about how the US would anything as a measuring system except the metric system? Same with paper.
I had the reverse, we had to get a ream of US Letter and corresponding envelopes sent over so we could ensure the layouts printed properly. Also some chequ… “checks” which were fascinating.
Couldn't they... just cut it according to A4 dimensions?
An interesting question, but I think it would be very hard to do it accurately. Also, some of the reports the needed to print during testing were looong.
Yeah, I’ve used a sheet of paper as a ruler too...
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.
The creators of metric weren't above buggering it to fit human scale needs.
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.
I don't think anybody loses sleep over the kilogram issue because, well, it's metric after all. A kilogram is exactly 1000 grams, so the gram is just as perfectly well defined. Nothing would really change if they were to promote the gram to be the standard unit of mass (not weight!) someday.
I am annoyed by it. We should be using gravs instead. Then there would not be this special unique unit with prefix as base unit.
There is also a C series of sizes which are slightly larger than the A sizes and therefore useful as envelope sizes.
Elegant, sure, but... fold a sheet of US Letter (8.5 x 11.0 inches) in half, and you're on your way to a pirate hat. Fold and pull it several more times, and you have a boat.
You can do the same with A4, of course. Metric and imperial pirates will have to battle it out.
Some Moleskine cahier notebooks are wrapped in a paper sleeve that has a ruler printed on the back. Inches on one edge; centimetres on the other (a slight improvement for non-American users over Field Notes notebooks, with a ruler on the inside back cover that’s inches only - also the sleeve is rather longer, 28cm in fact).
I recently went down the A4 paper sizes rabbit hole and found out that there is an ISO standard for this 'ISO 216'
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.
Same, last year. I like A4 for large notebooks, and B7nos the perfect size for a pocket journal but it is hard to find.
I have heard German toilet paper is A6, but I never got to verify that. If true, it's one of the more German things ever.
Almost. In Germany, standard tp is 100 × 140 mm, a bit smaller than DIN A6 (105 × 148).
I don't think it is, the aspect ratio seems off, but maybe I'm misremembering (not in Germany right now)
21cm is close to 20 which means A5 has a side close to 10.
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.
I always liked the Japanese idea of measuring room size by the number of tatami mats.
Fun fact: tatami mats are slightly smaller in Tokyo than in other parts of Japan.
Reminds me of older recipes that will say things like "can of tuna" or "can of beans" but what that means has changed somewhat.
A0 paper is for drafting. That's what people used for engineering drawings before we had AutoCAD with zoom.
Sqrt(2) being halfway between 1 and 2 multiplicatively, leads to interesting stuff. For example consider two integers A and B. They have a dual in the pair A+B and A-B. Well, not quite. You need to scale them down by 1/sqrt(2). If you do that to the duals, you get the originals again.
As the ratio used is a rational approximation of an irrational, I would guess that the ratio-preserving feature breaks down well before you get to atomic sizes, though I have neither proved that to be so nor figured out how to calculate the divergence.
If you have a Pro or Pro Max model of iPhone from the last several years, it has a LiDAR that allows the pre-installed Measure app to measure lengths/heights, etc., using the camera. Several higher end Android phones may also have the same.
> "Hold on. I think I hear another heckle. What is that? There are mobile phone apps that can measure things now? Really? Right. Security. Where's security?"
Just quoting the author here, haha.
Just a couple of days ago I used an A4 sheet to measure the area I had on countertop to see what size microwave I could fit in there.
Adds gsm issue to https://github.com/librasteve/raku-Physics-Unit/issues/32
Hint: The aspect ratio sqrt(2) should be quite convenient for foldable phones. Current ones seem to be more or less square if unfolded - what use case is that good for?
That would make the folded phone too wide though. More like a mini tablet.
ref: Huawei Pura x
>Like most sensible people with a reasonable sense of priorities, I do not carry a ruler with me wherever I go.
Let me introduce to you: the IKEA paper tape measure, folded neatly in your wallet.
Or just use your phones measuring App. So far the iPhone one has been precise enough for me when on the go.
Security!
(read the article)
I read the article, but is there any evidence suggesting the Apple measuring app is insecure? It only collects data not linked to you (usage data and diagnostics) and is using the same privacy policy as the Apple camera app, which pretty much every iPhone user is trusting already.
There's also the fact that if you don't have a convenient straight-edge around -- fold a sheet of paper, not too rough.
It's a good exercise in thinking, dhy that is so.
American: "Wow -- yet another example of practical math linked to everyday sources."
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."
There's also the fact that if you don't have a convenient straight-edge around -- fold a sheet of paper, not too rough.
What ... not everybody carries a small, 6' tape measure with them??? Surely I'm not THAT abnormal.
Most of the world carries a 2 m tape measure with them. You're only normal in the USA, Myanmar, and Liberia.
You can use objects of known length to measure other objects of unknown length. Am I a hacker, now?
Obligatory link to Markus Kuhn's excellent page on international/metric paper sizes: https://www.cl.cam.ac.uk/~mgk25/iso-paper.html
> We drink our tea from doughnuts.
Lol
Great video about human topology: https://www.youtube.com/watch?v=egEraZP9yXQ
Trying not to be too negative but this is quite a long blog post for what effectively just comes down to using a piece of paper to measure something, which I imagine lots of us have done in a pinch. Also, nit: one of the calculations on paper size seems duplicated due to a typo.
Personally I make sure to always carry around a string and some scissors, so any time I need an arbitrary measurement I can just cut the string to the length of the thing I want to measure (making sure to label it in case of multiple required measurements), then measure the cut string later. Simple.
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.
Maybe you could start off with a long string and then mark off its midpoint, the midpoints of the halves, and so on. Then you wouldn't have to cut a new string every time you want to measure something.
There's also the concept of a story stick.
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.)
This works fantastic for building furniture as well, where the absolute dimension doesn’t matter as much as all of the pieces having matching dimensions. A cabinet with drawers, for example. The story stick captures the spacing between the drawers, the width of the drawer, the slightly smaller height of the drawer face, etc.
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.
With carpentry in particular, it is extremely powerful to make multiple cuts at the same time -- set a fence once and then cut everything that needs to match at the same time, or stack multiple pieces together, or cut a board to length before ripping it into several pieces that need identical lengths.
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.
Was going to mention that too. 100% agree. If I mess up and end up needing to make matching cuts later on, I'll often set the fence using one of the existing pieces too instead of trying to re-measure. The story stick works great but lining up the teeth on the blade with the cut edge of an existing piece works fabulously well.
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.
What, and use the same thing to measure stuff anytime you measure something? Like that's ever gonna catch on! Next you're gonna tell me to use my lower arm as a measuring stick!
That's inconveniently long. Have you considered using your foot?
The span from my thumb to my pinky in a “measuring position” is 20 cm (and is easily repeated by moving the thumb to the pinky and then stretching out the pinky again). The length of my “thumbs up” hand is 16 cm. The width of my fist is 10 cm. The length of my pinky is 6 cm. The width of my thumb is 2 cm. This allows me to estimate distances between ~2 m and 2 cm pretty well. Knowing your foot/shoe length also comes handy sometimes.
> The span from my thumb to my pinky in a “measuring position” is 20 cm
26 cm for me. I can stretch to 27 cm quite easily, though.
> The length of my “thumbs up” hand is 16 cm.
18 cm.
> The width of my fist is 10 cm
Same.
> The length of my pinky is 6 cm.
7.5 cm.
> The width of my thumb is 2 cm
2.5 cm.
I guess the main thing between mine and more typical hands is my long, fairly slender fingers, then.
I do the same, but my piece of string has little lines and numbers telling me how long a thing is.
Reverse: perhaps carrying a measuring tape [0] ?
[0] https://www.amazon.com/Measure-iBayam-Measuring-Measurement-...
How long is a piece of string eh?
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
So besides the string and the scissors, you also need a marker that can write really, really tiny?
But this is also quite cool! These kind of articles are what makes HN interesting and fun.