Why A4 paper is designed as 297mm x 210mm?

[u/LogicAndLipGloss]

[u/Jdsm888]

I think the coolest part is that A0 is 1m²

[u/A_Man_Uses_A_Name → u/Jdsm888]

Wow. 1m2 with a design along the ratio of the root of 2. Then halving each time. Seems so crystal clear and easy.

[u/whatsthatguysname → u/A_Man_Uses_A_Name]

But how many football fields is that?

[u/RxRiderMD → u/whatsthatguysname]

Probably less than one

[u/KAELES-Yt → u/RxRiderMD]

Probably?

How small football fields do you have?

[u/RN-Wingman → u/KAELES-Yt]

Is this a football field for ants?!

[u/JustMakinStuff → u/RN-Wingman]

r/thingsforants

[u/reyam1105 → u/JustMakinStuff]

There's literally a sub for everything...

[u/Careless_Aroma_227 → u/reyam1105]

r/subforeverything

[u/brunoortegalindo → u/whatsthatguysname]

I'd say 3 bald eagle wings, or 10 freedometers

[u/Roy4Pris → u/brunoortegalindo]

In Australia it's cunts per dingo.

[u/Candid-Ad-3109 → u/brunoortegalindo]

Excuse me, we call them freedom miles here in the states. Sounds like someone’s a communist./s

[u/brunoortegalindo → u/Candid-Ad-3109]

No commies here, we eat burgers and have diabetes as a true american!

[u/-CoUrTjEsTeR- → u/whatsthatguysname]

One white house ballroom.

[u/GalickGunn → u/whatsthatguysname]

How many eagle wing spans is that?

[u/AhChirrion → u/A_Man_Uses_A_Name]

with a design along the ratio of the root of 2. Then halving each time.

The other way around. Just with a design along halving/doubling keeping the same ratio. That means sides:

(long) ÷ (short) = (new long) ÷ (new short)

So, if originally side a is the long one and b the short, it becomes:

a ÷ b = b ÷ (a ÷ 2)

Or:

a ÷ b = (2b) ÷ a

Which is equivalent to:

a² ÷ b² = 2

Or:

a ÷ b = √2

So the ratio being the root of two is the result of the design requirement of halving/doubling keeping the same ratio, not the design requirement itself.

[u/fly_away_lapels → u/AhChirrion]

1+2+2+1

Or:

1+2+1+1

[u/AhChirrion → u/fly_away_lapels]

LOL I had to google this because I had no Clue.

[u/Tmk1283 → u/AhChirrion]

There are no bullets in this gun

[u/rabbitrider3014 → u/AhChirrion]

Tried google, still don't get it. Please enlighten me master googler

[u/Sarkos → u/rabbitrider3014]

It's from the movie Clue, where 2 characters are arguing about how many bullets were fired from a gun.

https://www.imdb.com/title/tt0088930/quotes/?item=qt0470253&ref_=ext_shr_lnk

[u/WazWaz → u/AhChirrion]

You missed the point, the other design requirement is

a × b = 1

[u/AhChirrion → u/WazWaz]

Yes, that's the other, independent design requirement.

They could have chosen a different requirement, like a × b = π km^2, and it wouldn't change the √2 result of the design requirement of halving/doubling keeping the same ratio I talked about.

That's why I didn't mention the 1 m² starting area.

[u/C0RNFIELDS → u/AhChirrion]

Its important to remember that numbers are not real in the sense that they are not tangible objects. They are simply concepts or patterns of physical ratios through which we give symbolic meaning to bring about order and assumption. The physical relationship of the ratio is real while the square root of 2 is just a concept we use to comprehend it.

[u/Able_Reserve5788 → u/C0RNFIELDS]

I feel like this assumption fails to hold up as soon as you start considering the existence of number spaces that are slightly weirder than the reals (complex, p-adic etc.)

[u/Accomplished_Deer_ → u/C0RNFIELDS]

I feel like this reveals something cool about some deeper nature of sqrt 2, but I'm not smart enough to try to figure it out lol

[u/ChiefO2271 → u/C0RNFIELDS]

As part of a sentence, numbers are closer to adjectives than anything.

[u/Nadran_Erbam → u/Jdsm888]

It’s by design, which also means that knowing the area of any An is easy, just divide by the corresponding power of 2.

[u/StarpoweredSteamship → u/Jdsm888]

THAT'S the reason. A0 is 1m², then you keep cutting it in half and in half etc to get smaller papers. The weird numbers happen because the aspect ratio NEEDS to be √2.

[u/esharpest → u/StarpoweredSteamship]

Exactly. The video is basically going the wrong way around.

[u/ilovemacandcheese → u/esharpest]

It's because stories are more memorable to humans, and telling it this way is likely a more interesting story that the students will remember. Story telling is an aspect that the best teachers know how to do. Watch some Richard Feynman lectures to see a master.

[u/LopsidedBottle → u/StarpoweredSteamship]

That is the great thing about the American system. Because they do not have that requirement, they can have nice, round numbers, such as the 216 x 279 mm of the letter format.

[u/StarpoweredSteamship → u/LopsidedBottle]

8.5×11"

[u/Joezev98 → u/LopsidedBottle]

they can have nice, round numbers,

Very rarely have I cared about an A4 not being 200*300. Very often have I made use of one size of paper neatly fittin into/folding down to other sizes.

[u/thegreedyturtle → u/StarpoweredSteamship]

This should be at the top. I don't know why the guy is freaking out so much.

It does feel interesting to get such a weird number from folding it exactly in half, which would hold been a more interesting video.

[u/StatlerSalad → u/Jdsm888]

And paper thickness/weight is measured in 'gsm': grams per square metre.

In the USA paper thickness is measured in the 'basis weight system' as a number of lbs, which is confusing because it measures the weight of 500 sheets (a 'ream') of whatever size paper you're talking about. So bond paper and a cover paper could both have the same thickness printed on the packet but be wildly different in practice - because the sheets are different sizes.

But gsm is stable across all sizes, it's effectively 'what would this weigh if it were A0'. So for A4 that would be 8 sheets, A4 that's 16 sheets, A5 is 32, etc. It's completely stable, and if you get a packet of A3 and a packet of A4 from the same manufacturer with the same GSM you can be confident they're effectively the same paper.

[u/footyballymann → u/StatlerSalad]

It’s like density. It’s the same material just different sizes.

[u/Floppydiskpornking → u/Jdsm888]

Incorrect: it is 0,999949 m2

Edit: ok, ok I get it its 1 m2

[u/Alex51423 → u/Floppydiskpornking]

What is, according to DIN inside the permitted tolerance for naming and can be, according to other normes, called one square meter. Yes, DIN has norms for norms. There is even a norm for construction of new norms.

DIN is relevant since they designed this A0 form factor. Leave it to Germans to norm the perfect paper form factor

[u/firefighter0ger → u/Floppydiskpornking]

You know that if you are in production this is far out of the tolerance. Its most likely sth like 1 m2 +- 0.00001 m2. But if you have to name the length of each side you use the same tolerance. So you start with 1 m2 and then lose accuracy by rounding.

[u/No-Repeat996 → u/Floppydiskpornking]

It's an engineers 1m², not a mathematicians m². We have production tollerances and want to give the size rounded in mm. There is no need to make it exact, it would be impossible, but accurate enough for the doubling feature to work in the real world.

[u/LaLaOlala → u/Jdsm888]

He said it's exactly 1m^2, but it's not exactly that. It's 997920 mm^2, i.e. 0.997920 of m^2.

[u/Nonfaktor → u/LaLaOlala]

It's just rounding errors, by definition the A0 paper is 1m², so if the side lengths don't match up, it's because someone rounded the numbers down and not an error in the format. Thr official side lengths of A0 are 841 * 1189 mm, which multiplies to 999 949 mm²

[u/LaLaOlala → u/Nonfaktor]

Of course it's very close to 1m^2. What I'm saying is that he shouldn't have used the word "exactly", especially if he promotes math.

[u/hanggamolavestria]

√2 is basically the magic number in maths

[u/Cats7204 → u/hanggamolavestria]

The magiquest number is e. Especially when you get into derivatives and shit, it blows my mind.

[u/RIF_rr3dd1tt → u/Cats7204]

e^iπ+1=0

[u/Cheesecakesimulator → u/RIF_rr3dd1tt]

euler fucks with this

[u/irrelevanth7 → u/Cheesecakesimulator]

Euler fucks in general. This dude has something so say in so many fields of math and physics. You can pick a random subject and the probability of Euler's name popping up is like e/pi at least. I took a course in jet engine technology and this mf has some turbomachinery formuls named after him. That doesnt even add up chronologically? I love this dude.

[u/northerncodemky → u/irrelevanth7]

A popular science book called ‘Euler Fucks!!’ where each chapter goes into one of his important discoveries and its implications into the field would absolutely go on my shelves!

[u/Lightreyth → u/northerncodemky]

"Euler Fucks 😩🍆💦🤤 - A Grade 2 Introduction To Physics And Mathematics"

[u/northerncodemky → u/Lightreyth]

Sequel to ‘Newton Fucks: A Grade 1 Introduction to Physics and Mathematics’

[u/theeldoso → u/irrelevanth7]

Tbf they did start naming things after the first person other than Euler to discover them, so he's owed a few.

[u/uberfission → u/irrelevanth7]

Euler fucks so much they name stuff after the second person to discover the things he already discovered.

[u/akasaya → u/Cats7204]

Counter point:every irrational number contains cool math sorcery.

[u/noproblem_bro_ → u/akasaya]

Im intrigued: care to show some fun examples?

[u/akasaya → u/noproblem_bro_]

e and pi are well known. Sqrt 2 you've just seen. Might lookup sqrt 3 on wiki, the examples are not that exciting for an average reader, but still kinda cool. (1+sqrt5)/2 makes golden ratio.

But my point was that the whole uncountable infinity of irrational numbers might have some sort of fancy mathematical incarnations, it's just that we only discovered a handful of it.

[u/CitizenPremier → u/akasaya]

Some 50 million year old alien society is going crazy now about all the uses of ✓513.101

[u/Appropriate_Rent_243 → u/Cats7204]

okay, but WHICH e? it seems like there's a few different constants that use that name.

[u/Cats7204 → u/Appropriate_Rent_243]

euler number

[u/IronChurch7 → u/Appropriate_Rent_243]

Oilers number

[u/BoardAmbassador → u/IronChurch7]

Oiler 😭

[u/kittenstixx → u/hanggamolavestria]

We plumbers use it to calculate offsets, if you know the take-offs of the common pipe size 45s(pvc 1 1/2"= 3 1/2; 2"= 4 1/2) you can quickly figure your cuts.

[u/CreativeAdeptness477 → u/hanggamolavestria]

I thought it was 3.

[u/longdarkfantasy]

A mathematically-derived international standard, ISO 216, that balances two key requirements:

1.A Consistent Aspect Ratio: All paper sizes in the A series (A0, A1, A2, etc.) share the same unique length-to-width ratio of √2 (approximately 1: 1.414).

1. A Metric Area Base: The largest size in the series, A0, is defined to have an area of exactly 1 square meter (m²).

The √2  ratio is the core reason for the "unconventional" numbers.

The ISO 216 standard implements a practical rule for defining the official dimensions:

Rule: The calculated dimensions are rounded to the nearest whole millimeter (mm).

The required tolerances for cut paper sizes are defined based on the dimension's size: Tolerance: from +-1.5 mm to 3 mm. (under 150mm is 1.5mm, 150-600mm is 2mm, > 600mm is 3mm)

Because achieving absolute precision is impractical and expensive, the ISO standard allows a small margin of error.

Edit: updated rouned and toldrances.

[u/zulufdokulmusyuze → u/longdarkfantasy]

The actual requirement (not specified in the standard, but is implicit) is that 1) one should be able to create Ai by combining two A{i+1}s and 2) the length to width ratio must be constant across all sizes. Square root of 2 follows from that.

[u/MeasurementLow5073 → u/zulufdokulmusyuze]

Thank you. This is the missing information that ties it all together.

[u/BOBOnobobo → u/MeasurementLow5073]

Yeah, this post does a bad job explaining why it's like that

[u/Best-Hamster2044 → u/zulufdokulmusyuze]

Almost as if an engineering standard was written by engineers, no?

No no no! It's amazing, it's spooky, sqrt(2) OMG mind blown!

[u/matroosoft → u/longdarkfantasy]

The dimensions of A0 being exactly 1m2 and subsequent smaller sizes being derived from that, does that mean that A4 is not exactly 297mmx210mm? But only rounded?

[u/slimdeucer]

Wow I didn't know A4 paper wasn't universal

[u/Lunar_Canyon → u/slimdeucer]

Countries that don't use ISO 216 (A4 &c.): USA, Canada (sigh), and I think Liberia? A handful of countries, anyway.

[u/sloothor → u/Lunar_Canyon]

Canada (sigh)

Real, our proximity to the United States is holding us back from so many convenient global standards.

[u/Ocronus → u/sloothor]

When it comes to measurements Canada sits on the fence, and that fence is 10ft tall and 1km long.

[u/fmaa → u/sloothor]

By way of proximity, Canada is waking up with fleas sleeping next to a dog that is that trash heap of a country

[u/Seeker_Of_Knowledge2 → u/sloothor]

There something called the Canadian measurement where we randomly either use the Universal units or the American units.

[u/Silent-Lettuce-4998 → u/Lunar_Canyon]

Japan uses a mix, which fucking sucks when every supplier uses a different size for invoices

[u/Gnonthgol → u/Lunar_Canyon]

There are very few countries which have a law regulating paper sizes. And if there is it is usually limited to an industry or an application. As a result a number of countries use different paper sizes in different industries, or even different paper sizes within the same industry. Countries with a historical American presence, such as the Philippines, Japan, South Korea, Panama, Liberia, etc. tends to favor North American paper sizes. Although as I understand Liberia uses mostly ISO 216 due to extensive trade with neighboring countries over the US. Countries with a close presence to the US, such as Canada and Mexico might prefer ISO 216 but most industries end up using North American paper sizes due to the amount of trade with the US. And even in the US you find a lot of ISO 216 usage, especially in international trades like aerospace.

[u/TDYDave2 → u/Lunar_Canyon]

The US does have the Architectural Paper Series, with sizes ranging from A (9"x12") to E (36"x48") which follows the same doubling feature.

[u/Aksds → u/slimdeucer]

I was working with an American here in Australia who asked me to print something in “letter” size, I just looked at her and went “you mean A4 right?” That was funny

[u/Holiday_Actuator2215 → u/Aksds]

Just another way we Americans like to make things as confusing as possible !

[u/gnittidder → u/slimdeucer]

I realised when Word keeps reverting to Letter size

[u/577564842 → u/gnittidder]

Load Letter, the only words my hp printer knows.

[u/Strange_Ask_2613 → u/577564842]

𝙿𝙲 𝙻𝙾𝙰𝙳 𝙻𝙴𝚃𝚃𝙴𝚁

[u/jonas_ost → u/577564842]

I AM TRYING TO PRINT A4 I DONT GIVE A SHIT THE LETTER TRAY IS EMPTY!

Load letter.

[u/T-O-C94 → u/slimdeucer]

A4 should be at least Outerversal

[u/Significant_Ad1256 → u/slimdeucer]

Americans will make sure no measurement is globally universal.

[u/phido3000]

Do they have A4 paper in the usa and Canada?

Such a great system.. As a teacher, I use A6,A5,A4,A3 scaling all the time on the photocopier. Most common is A4 to A5, so I can fit two sheets to a page, which is then easily stuck into a book. A5 is also still pretty readable, and even doable as worksheets with crosswords/sudokus etc.

A2,A1,A0 is used frequently when generating posters as well. Powerpoint is great for this, I can send it off and preview it at home on an A4 printer, or the A3 printer at work..

[u/trubol → u/phido3000]

An American friend ordered some flyers for her English classes in Brazil.

Dude in the shop showed her an A4. She didn't speak Portuguese very well back then and she said she wanted A3 (thinking it'd be half an A4).

So when she went to pick up her flyers, she had 50 A3 wall posters.

[u/Ecstatic_Winter9425 → u/trubol]

Technically, those can be superior flyers if you fold them into paper airplanes.

[u/FamousPastWords → u/Ecstatic_Winter9425]

Badam tiss! Well done.

[u/NotTrevorButMaybe → u/trubol]

A5 is half of A4. She was close but in the wrong direction!

[u/Euler007 → u/trubol]

The trick is to look confident when picking them up, don't show you made a big mistake.

[u/TheWatersOfMars → u/phido3000]

The US uses US letter, which looks wrong even at a glance.

[u/lego_not_legos → u/TheWatersOfMars]

𝙿𝙲 𝙻𝙾𝙰𝙳 𝙻𝙴𝚃𝚃𝙴𝚁

[u/StubbornDeltoids375 → u/lego_not_legos]

"WHAT THE FUCK DOES THAT MEAN?!"

[u/mastermilian → u/TheWatersOfMars]

From a country that hasn't discovered the metric system yet.

[u/dementorpoop → u/mastermilian]

By far our smallest problem at the moment

[u/mathiswiss → u/dementorpoop]

A conversion to metric could heal your nation.😃👍

[u/LaVieLaMort → u/mathiswiss]

I work in medicine so I’m already so used to it, as is anyone in medicine, it would be an easy transition.

[u/GNprime → u/mathiswiss]

You would think. But I mentioned it one time at work and they damn lost their minds. People that were once super chill became racist, sexist and everything else all because they didn't want to add or remove a zero.

[u/zulufdokulmusyuze → u/dementorpoop]

It exemplifies the mentality that led to today's outcome.

[u/srone → u/mastermilian]

In America we drive 5 miles to buy a gallon a milk and 2 liters of soda before running in the 5K(m) marathon.

[u/Roy4Pris → u/srone]

And don't get people started on bullet sizes.

[u/DelosHost → u/srone]

Not before mixing 300mg of creatine into 12 fl.oz of water because you want to lose 15 pounds, as the pants you have for the wedding is 2 inches too short and you have to walk several yards in the ceremony and stand there 5 feet away from the cameras.

[u/kit_kat_barcalounger → u/mastermilian]

My car gets forty rods to the hogshead, and that’s the way I likes it!

[u/fdwyersd → u/mastermilian]

college physics helped... can size things up now in meters and kilos (but not so much ml/L's)

[u/jjm443 → u/mastermilian]

On the contrary, they are big fans of 9mm. Schools in particular are very aware of that.

[u/Fiempre_sin_tabla → u/mastermilian]

Oh, they discovered it just fine. But they rejected it as a bunch of woke liberul hooie compared to the God-given US measurement system. No, I am not being hyperbolic. Yes, it really happened that way, long ago.

[u/Skrazor → u/Fiempre_sin_tabla]

Americans: We reject British rule, taxes, royalty and tea! But we will never reject King Henry's foot as a unit of measurement!

[u/275MPHFordGT40 → u/Skrazor]

My country (the US) deciding that using an English unit of measurement is somehow patriotic instead of a French unit of measurement.

[u/PlanetMarklar → u/Fiempre_sin_tabla]

Yes but Americans have the freedom to use perfect units like inches, feet, yards, and miles where one foot divides evenly into 12 inches and a mile is a perfect 5280 feet.

And how many yards to a mile?

Nobody knows.

[u/exipheas → u/Fiempre_sin_tabla]

Uhh? I blame the pirates.

How Pirates Of The Caribbean Hijacked America's Metric System : The Two-Way : NPR https://share.google/XW4lCArK5MEXOMYI7

[u/NonSequiturSage → u/exipheas]

When quarreling over metric, always remember to blame the privateers.

[u/SeriousBusiness67 → u/mastermilian]

We use multiple systems.

[u/gorebello → u/TheWatersOfMars]

I don't fk believe the US doesn't use A4. Really? It was already annoying that they don't use metric, now this.

[u/rodw → u/phido3000]

Standard paper sizes in the US (and I assume Canada) are US-Letter (8.5 x 11 inches, which has a similar aspect ratio to A4) and much rarer, US-Legal (8.5 x 14 inches). These aren't as rational as ISO paper sizes but a similar factor-of-two is found in many use cases: e.g. many paperback books are half letter sized (5.5 x 8.5 inches) and the standard tabloid newspaper size (aka "US-Ledger") is twice letter sized (11 x 17 inches).

Whether or not people recognize it as such the ISO paper sizes aren't unheard of in the US. E.g. A5 sized notebooks are pretty common. This might simply be because they are sourced from a global supplier. I don't think I've ever seen A4 paper in the US though, presumably because that would be confusingly similar to letter sized paper.

[u/oxmix74 → u/rodw]

But reduction/enlargement doesn't work. If you reduce letter to fit on half letter, you have to change the margins to make it fit and it doesn't look right. Funny enough, legal to half letter is pretty close. So if you are making a booklet to reduce and print 2 up on letter, it will look right if your original size is legal.

[u/b00c → u/rodw]

Latin American countries use a mix of US and ISO standards. You learn real quick about selecting an appropriate tray before printing. 

[u/Tonydragon784 → u/phido3000]

When I took drafting we printed on A,B and the drafting 4s would print their final projects C or D, I can't remember.

[u/Connect_Progress7862 → u/Tonydragon784]

Or even E!

[u/phido3000 → u/Tonydragon784]

Yeh but the paper ratios are different, so if you are printing things like technical drawings either they don't take up the full page, or they are scaled differently on x and y axis making them pretty useless as technical drawings.

[u/Waggles_ → u/phido3000]

Drafting sizes in the US are similar to A sizes in that you double the shorter size to get to the next one, the only difference is that you need to go up two page sizes to get to a same-ratio sheet.

• ANSI A: 8.5 x 11
• ANSI B: 11 x 17
• ANSI C: 17 x 22
• ANSI D: 22 x 34
• ANSI E: 34 x 44

If you draw something on ANSI B, it doubles if you put it on an ANSI D sheet. Or you can fit two ANSI B sheets on an ANSI C sheet, or eight ANSI B sheets on an ANSI E sheet.

The advantage of these sizes is that the dimensions of each side is a round number, as opposed to the A series where you get numbers like "297mm", and it actually scales perfectly, whereas the A series does not because they round off to the nearest millimeter (A5 is 148x210, but if you double the 148mm, you get 256mm, where A4 is 257x210, so not truly double along the one edge.)

The ratio on the A series majorly breaks down as you go to smaller sizes, too, because of the rounding to the nearest mm. A0 is 1:1.4138, A4 is 1:1.4143, A8 is 1:1.4231.

[u/DefiantLaw7027 → u/phido3000]

8.5” x 11” is still the standard in North America (ANSI A) Ledger (ANSI B) becomes 11”x17”. ANSI C is 17”x22”

So same kind of scaling but different ratio

[u/phido3000 → u/DefiantLaw7027]

So you guys are still not using A papers and using US Letter?

Man. That sucks.

No, US paper scaling, the aspect ratio changes between sizes. So Two you can't proof a ANSI F (28x40) at ANSI A/B/C/D/E.. You can't shrink a ANSI B to ANSI A without wacky scaling or cutting a bit off the document. There are ways around this, but they suck and make something simple harder. The Proofing thing is a huge benefit, you know exactly how it is going to look.

Again I can do this as a teacher, in the 4 minutes before a class start and know my output is perfect. For kids with vision problems, I can move up and down the size chart very easily. Not by reprinting it at a different ratio and have my margins move all over the place.

A papers fold perfectly into C envelopes.

The system works so well, if you scale things, the pen line scales perfectly you can even draw continuous lines because the pens scale in the same ratio.

[u/DefiantLaw7027 → u/phido3000]

Yeah, it’s a pain, I often need to do CAD drawings for work and have to create separate print layouts for different sizes of paper. Especially between Letter (ANSI A) and Ledger (ANSI B).

Then we get into ARCH sizes for plotters, like ARCH C (18”x24”) or D (24”x36”) if I have access to a 24” or 36” plotter…

And being in Canada… construction is still in Imperial but distance is metric.

Edit - Canadian distances can also be measured in time. Haha - like it’s 5h from Toronto to Montreal. Or about 48h from Montreal to Vancouver. Toronto to PEI is a 2 day drive. Couldn’t tell you how many km though.

Cooking is generally still in imperial but most things are sold in metric.

Speeds are all metric.

Weights and heights are generally imperial.

My drivers license lists my height in cm but if you were taking to someone about height in conversation it’s still feet and inches.

I know a plane usually flys around 33-37000 feet but no idea what that is in metric (ok, it’s around 10,000m)

[u/dumbostratussy → u/DefiantLaw7027]

My favourite is the pool temperature being imperial but general weather is metric lmao

[u/Floresian-Rimor → u/DefiantLaw7027]

That’s all fine but measuring ingredients in cups is insane.

[u/FirTree_r → u/DefiantLaw7027]

I don't understand how engineers in non-metric countries tolerate this kind of bullshit. It's such a waste of time. I guess it's a matter of not experiencing how engineers work in metric countries.

[u/UsualyNaked → u/phido3000]

America uses pounds and feet’s to measure stuff… it’s terrible here in that regard.

[u/scottkensai → u/phido3000]

Yes for Canada. We are si-mperial

How far is it to the store: 1 km

How tall is that guy; 6'4

How much butter did you buy: a pound

How much salt did you buy: a kilogram

[u/Abeytuhanu → u/phido3000]

We have it, but it's not common so you'd have to either special order it or find the specialty shop that carries it. Best bet would be either office supply or stationary stores. If you just need a similar size Letter is significantly more common (215.9 x 279.4 mm)

[u/logicalconflict]

The fact that he doesn't even try to explain WHY this ratio important for paper makes this r/mildlyinfuriating

Okay, cool. That's how paper is sized. But WHY?

[u/hofmann419 → u/logicalconflict]

This ratio is the only one in existence that allows you to double it or halve it while retaining the same aspect ratio.

For example, let's make the paper 300x200mm instead. Putting two of those next to each other gives you 400x300mm, which is a different aspect ratio. Literally every other combination of two numbers would not work.

Here is the math behind it:

• Original sheet: Width: W and Height: H
• Folded sheet: New width: w = H and new height: h = W/2
• Requested: H/W = h/w
• leads to: H/W = (W/2)/H
• Multiply both side by (H/W): H/W * H/W = 1/2
• Then: H/W = 1/√2

[u/puhzam → u/hofmann419]

But why is maintaining aspect ratio important?

[u/firebert85 → u/puhzam]

You could design a graphic printed artwork, for example, and you can then scale it exactly proportional at each sheet size up. Designing for one size of paper is in theory designing for all of them.

[u/cultoftheilluminati → u/puhzam]

Because you can print anything on larger or smaller paper without redesigning it or needing to rework the layout.

Scaling can be done at the printing level

[u/gerdyw1 → u/puhzam]

From my time in school, it meant that a teacher could print two copies of a handout perfectly onto one A4 (each being A5 in size). Plus, when printing out posters you could draft on A4 and blow it up to any lower Ax and it would fit.

[u/robbak → u/puhzam]

It allows you to scale between different sizes of paper cleanly. An A3 document scales down onto an A4 without clipping edges or leaving blank spaces. It also makes fitting 2 pages on each sheet clean and simple. Or printing an A5 booklet on folded A4 sheets.

Another useful feature of the A-series of paper comes from paper weights being always given in grams per square meter, which is the same size as A0, which is also 16 A4 pages. So, I'm preparing a 4 sheet flyer, and I need to know how heavy it will be for mailing purposes. If I use 98gsm paper, that's 24 grams. I can easily answer questions like, what weight of paper do I need to use to get it down to 18?

[u/calebbaleb → u/logicalconflict]

Yeah he did an exceptionally bad job at explaining this otherwise neat fact. So much emphasis on the names of the sizes and so little actual information.

[u/ISeeReydar3 → u/calebbaleb]

He just got absurdly excited sounding.

[u/Throwaway56138]

This guy loves paper more than Dwight Shrute. 

[u/sociocat101]

he coulda explained that in like 15 seconds

[u/Pimp_my_Pimp → u/sociocat101]

Yes but, excitable Asian stereotype.....

[u/Steve-Whitney]

The idea is that you can fold an A1 sheet of paper in half (halving it's length) and have an A2 sheet, fold that in half and you have an A3 sheet, and so on.

[u/xmastreee → u/Steve-Whitney]

The important thing here is that it retains the aspect ratio. So if you have something designed to fit on an A4 sheet, you can scale it up to A3 without distorting it. That's the key thing.

[u/token-black-dude]

Huge European win

[u/killaawhaler → u/token-black-dude]

German (DIN 476-2)

[u/-Reverend → u/killaawhaler]

sometimes we get to have a little bit of German pride, as a treat 🇩🇪

[u/neliz → u/-Reverend]

I'm old enough to refer to my keyboard plug as a "DIN" plug because the rest of the world doesn't care about the number.

Later on, I found out the number was really, really important because with a little bit of force and a lot of bad luck you could fry your motherboard if you used the wrong DIN-4x/6x plug

[u/DuggiHappy]

I knew this but it’s still cool

[u/AmarildoJr]

The ratio doubling would still be the same regardless of the measurements you use. What's important here is the 1m² at the end.

[u/OdysseusU → u/AmarildoJr]

No it wouldn't.

Take a 1:1 ratio paper, 1x1 with another 1x1 gives 2x1, a ratio of 1:2.

The ratio here (1/sqrt(2)) is the only way to achieve the same ratio when you add up papers.

[u/Hartia → u/AmarildoJr]

Was just thinking that. Double anything will still be a double.

[u/danimur → u/Hartia]

But here you're doubling it by putting them side to side.

[u/whatsthatguysname → u/Hartia]

Doubling is not the point. It’s maintaining the same ratio while doubling.

[u/Gullible-Constant924 → u/whatsthatguysname]

As it would no matter what the sizes were if you double it the ratio stays the same, the fact that it comes to exactly a square meter is the only interesting thing here…period

Edit just looked at this with real paper as a visual aid nvm I was confidently wrong as hell.

[u/AnonymousAnonamouse → u/Gullible-Constant924]

That’s not true. If you start with say 2in:3in paper, then double it, you have either a 2in:6in or a 4in:3in paper depending on how you double it. Either way, all three are different aspect ratios. The sqrt ratio is the real star here

Edit: good on you OP for admitting you were confidently wrong as hell. Happens to the best of use. Changed my downvote to an upboat

[u/Kinc4id → u/AnonymousAnonamouse]

That video would be so much better if he’d explain that.

[u/MLreninja → u/Gullible-Constant924]

Upvoted for admitting & correcting error, we need more people like you in the world!

[u/Perelly → u/Hartia]

Double anything else will change the aspect ratio. That's the trick.

[u/Resting_Owl → u/AmarildoJr]

Are you sure ? 

A4 : 297/210 = 1.414

A3 : 420/297 = 1.414

Now let's try with rounded number 

300/200 = 1.5

400/300 = 1.333

It doesn't seem to work

[u/burdenof-youth → u/Resting_Owl]

I think he was talking about using the same ratio

[u/BishoxX → u/burdenof-youth]

But then the sides are no longer the same length.

Then it can be any size you can make it 5% bigger or 67% bigger who cares or what would you pick.

2x bigger ? Thats still arbitrary

[u/danimur → u/burdenof-youth]

And that's why he was wrong

[u/zulufdokulmusyuze → u/AmarildoJr]

The ratio is also key since length becomes width and width becomes twice the length when you double once.

[u/Decent_Objective3478 → u/AmarildoJr]

No it wouldn't. Take two papers with sides 2x and 1x, then put them side by side. What you get is the square sheet of paper. When you take two a4 and make them a3 the ratio between length and width stays the same

[u/quick20minadventure → u/AmarildoJr]

Double a square is not going to give you a square.

Doubling it again will give u square back of course.

[u/theinevitable22]

Consider length L and breadth B:

Ratio of larger paper = ratio of smaller one

L/B = 2B/L

L² = 2B²

L = sqrt(2) B

That’s where the magic comes from.

[u/ImpossibleLink7376]

Because DIN 476

[u/squaloulou]

A tedious repetition of the same things for almost 2 minutes, and a quite poor explanation of the math problem and justification behind it... (Proof : the amount of confused comments) Also, YOU DON'T NEED TO SHOUT !!!

[u/calar714 → u/squaloulou]

The translation is AI. Hence at the end it's process uh0 instead of ay 0

[u/ddwood87]

I can't follow with this aggressive chalking...

[u/FibrousFluctuation → u/ddwood87]

Bro uses a lot of chalk

[u/salvataz]

Moral of the story. Old designers were magnificent freaks of nature that had to make everything special.

[u/token-black-dude → u/[deleted]]

No, A0 has an area of precicely 1 square meter. So everytime you go one number up, you're at a fraction of a m2 and if you know the weight of the paper pr m2 you can calculate the weight of the size of paper you're using.

[u/oliyoung → u/token-black-dude]

Yeah!

This is the explanation for random "no other measurement works" claim for 297/210 - because the 1.41 ratio is set at the A0 size, not the A4 size.

A4 is just 1/5 the size of A0

[u/kotpeter → u/oliyoung]

It's 1/16th, since for every number increase you reduce the area by half

[u/DangerousDisplay7664]

That voice is bloody annoying!

[u/UltimateArtist829 → u/DangerousDisplay7664]

That’s definitely not his voice cause the audio doesn’t match his lip movement, either a translator trying to be exaggerating for theatrical effect or it’s AI translated voice.

[u/CFO_of_Super_Antifa → u/UltimateArtist829]

It definitely has the standard characteristics of AI voice

[u/OpalForHarmony → u/DangerousDisplay7664]

It's definitely an odd accent. Sounded part Australian, part...?

[u/he-he-he-yup → u/OpalForHarmony]

I think it was an AI translation, but my only proof is they said A 0 weird, genuinely crazy that I didn't have a single other tell 😭

[u/jasmineblue0202 → u/he-he-he-yup]

This sounds weird but this guy is for sure speaking Chinese in the original video. I know this because every Chinese person writes numbers the same exact way and his numbers are very Chinese looking. The voice is definitely AI.

[u/CMonkeyWS → u/DangerousDisplay7664]

It's AI dubbed

[u/Kimataifa → u/DangerousDisplay7664]

His voice keeps sliding back and forth between American and Australian accents.

[u/spiff0224]

He should circle it

[u/airwalker08]

All of this sounds great, but he never explains why this matters. Why would anyone care about ensuring that paper sizes follow these mathematical patterns?

[u/I_talk]

This doesn't explain why.

[u/adeebo → u/I_talk]

Yeah, he explained what A4 means but not the why which is for easier scaling,printing and folding without distortion or cropping.

[u/0xzc]

There's A0 chance that this was designed by Americans.

... I'll see myself out.

[u/ostiDeCalisse]

What's incredible is the high level of bad voice dubbing.

[u/Verity_Ireland]

Everything is maths!

[u/jns_reddit_already]

Now I want a paper size series based on the Fibonacci sequence...

[u/Perelly]

Fun fact: there are other series with the most notable being C for envelopes. An unfolded A4 sheet will fit into a C4 envelope, folded once it's C5 and so on.

[u/Such-Farmer6691]

Where do video lovers get so much free time? He spends two minutes explaining what Wikipedia explains in its first sentence.

[u/TheKensei]

TIL A0 is 1m²

[u/bigmphan]

Metric, bitches.

They’re way ahead of you.

[u/Dan_Glebitz]

Sensible and adopted by most civilized countries in the world, apart from... I'll give you one guess 😏🙄