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.
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.
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.
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.
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.«
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.
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.
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.
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.
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.
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).
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.
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.
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...
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 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.
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.
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[ 4.6 ms ] story [ 71.6 ms ] threadNitpick: typo in the dimensions for A3.
Letter paper, credit card, banknote, business card, etc.
Better than an average square, better than an average ruler.
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.
"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.
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.
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
[0] https://www.youtube.com/watch?v=zDKBCIMkDbw
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.
So really, how absorbant the paper is should be the gold standard, so let's ask manufacturers to put that on the packaging?
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.
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...
It's a good exercise in thinking, dhy that is so.
Lol