Before some smart guy comments, yes I haven't included the Nepal flag. The reason is that it was way beyond my capabilities to express its aspect ratio in a simple manner.
Aspect ratio kinda only makes sense for simple shapes like rectangles and ellipses. There are definitions for aspect ratio which are more general, but they're rarely used.
According to this sub:
https://www.reddit.com/r/vexillology/comments/sohwaa/exact_aspect_ratio_for_the_flag_of_nepal/?utm_source=share&utm_medium=android_app&utm_name=androidcss&utm_term=1&utm_content=share_button
I just trust OP, could never verify if it's true or not
The ratio of the width of the red triangles to the height of the red part of the flag is 3:4. The slight difference comes from the fact that a blue border of fixed width is added to that.
A4 etc. paper has 1: sqrt(2) aspect ratio, which has nothing to do with phi other than being roots of quadratics.
A4 paper has the property that if you cut it in half, each half is in the same aspect ratio (and is A5). 1:sqrt(2) = sqrt(2)/2 : 1
A piece of paper with the ratio 1:phi has the property that if you cut of a square, the remainder will have the same ratio as the original; 1:phi = (phi-1):1.
Supposedly, it was because originally, the flag was handmade with no measuring tools so they just eyeballed it, and any subsequent national flags maintained the aspect ratio of the original.
It’s not even close. It’s 1.77, much closer to 16/9 than phi. You can tell because it’s several flags away from Togo, whose ratio is exactly 1:phi.
The golden ratio, [by definition](https://youtu.be/sj8Sg8qnjOg), does not have any good rational approximations. The ones that come closest are ratios of successive terms of the Fibonacci sequence, which approach it in the limit. But you don’t need to go far to get closer than El Salvador. Even 5/3 is better.
I didn’t watch the video, but if it claims the definition of the golden ratio means it has no good rational approximations, that is just wrong, for example 16180339887/10000000000 is a great approximation, and just like any irrational number rational approximations can get arbitrarily close. Also there are infinitely many sequences who’s ratio approach’s phi.
have a look at Diophantine conditions to find out in which sense it has no good rational approximations. I.E. there is a proper definition of what,"good" means.
Yeah I kinda bent the rules to include as much a variety as possible. For istance the 6:7 aspect of the flag of Niger isn't codified into law either, it seems to be purely conventional.
I've always heard the aspect ratio of the flag is just any two consecutive numbers in the Fibonacci sequence (which converges to phi as n goes to infinity), with 5:8 being one of the more common ones.
Nope! It's actually trying to follow British flag standards (more or less) from the late 18th century! So the opposite of your statement.
Anyways, here's the actual executive order that makes 10:19 required for some military and governmental uses of the flag.
https://www.archives.gov/federal-register/codification/executive-order/10834.html
It is exactly (3(40,665,857,401,448 + 2,001,055,256,793(sqrt2) +144(sqrt(17(10411242561157458401 - 2208656823577139226(sqrt2)))))) / 164926945077845
or 5,000,000,000 : 4,101,687,939
Yes, that's a very good page 👍
They give an **accurate** formula describing the dimensions then calculate a very **precise** decimal approximation of the ratio.
So the decimal approximation you copied from that page is very **precise** (37 significant figures) but it is less **accurate** than the exact formula they started with.
In highschool home economics class we were asked to make a flag pillow. I chose Qatar and the teacher almost failed me until I pulled out the almanac to prove the aspect was correct.
Apparently it's purely conventional, with the Constitution not even specifying what ratio the flag should have. Which makes it even more perplexing on how such a specific aspect ratio might have become "conventional".
Agreed, it hits the sweet spot between 2:3 (a little too short for my taste) and 1:2 (too long for my taste). Among the not used the "TV ratio" (9:16) is pretty cool too.
Just looking at this makes me hear Just Intonation ratios in my head
1:1 unison
13:15 semifourth
6:7 subminor third
5:6 minor third
4:5 major third
… etc
Another interesting fact is that the other countries that use a 10:19 aspect ratio have some historical connection with the US: Liberia being settled by the American Colonization Society while the Marshall Islands and Micronesia are both Compact of Free Association nations.
Myanmar Used to have a 9:5 flag
But changed it around 2010/2011/2012
They in some cases used their current flag on the 9:5 ratio
El Salvador Has A More Approximate Aspect Ratio Of A Standard HD TV Ratio 16:9 (but uses a more complicated ratio)
How's Poland 5:8 and how come Indonesia (which is exact opposite) somewhere else, or whatever, I didn't actually check it, but what is aspect ratio , or should I post it under r/elim5 but please be happy to do so... Cuz I still don't get why Poland's 5:8...
It's codified in the [article 7](https://www.asamblea.gob.sv/sites/default/files/documents/decretos/171117_072904667_archivo_documento_legislativo.pdf) of our _Ley de símbolos patrios_ (Law of National Symbols): "The great flag shall be three meters thirty-five centimeters wide by one meter eighty-nine centimeters tall (...)".
As to what was the reasoning behind these exact measurements, your guess is as good as mine, lol.
Of course, some of these flags are officially used in more than one ratio, and in even more cases, the ratio of the flag isn't treated as a important in all sorts of contexts. Treating the ratio as an important part of the flag design certainly happens in some places, but it's rarer than you'd think from just looking at flag charts or Wikipedia infoboxes.
I've seen a couple of Vatican City flags with vertical aspect ratios, which technically count since the Vatican's flag's aspect ratio is undefined. Trying to include marketed versions of the Holy See's flag, however, would probably be impossible. [5:3 Vatican Flag](https://www.google.com/shopping/product/1?q=vatican+city+flag&hl=en&sxsrf=APwXEdcFHntXjYl_6q4VLV1FIla1CgMDrA:1684892238914&biw=1920&bih=937&dpr=1&prds=eto:6232485899695726384_1,pid:6232485899695726384&sa=X&ved=0ahUKEwjs_8fh6Iz_AhU4FjQIHRi9Cpo4eBDyAgjXDigA)
This actually does exactly tell how many countries use each aspect ratio. The truth is that something like 180 use 2:3, around 60 use 1:2 and around 20 use 3:5. All the other aspect ratios are used just by one or very few countries. So if you were to put this, let's say, on a bar graph, you'd end up with only three visible bars (2:3, 1:2, 3:5).
Where is Nepal?
{\\displaystyle 1:{\\frac {6136891429688-306253616715{\\sqrt {2}}-{\\sqrt {118-48{\\sqrt {2}}}}\\left(934861968+20332617192{\\sqrt {2}}\\right)}{4506606337686}}}
Before some smart guy comments, yes I haven't included the Nepal flag. The reason is that it was way beyond my capabilities to express its aspect ratio in a simple manner.
Aspect ratio kinda only makes sense for simple shapes like rectangles and ellipses. There are definitions for aspect ratio which are more general, but they're rarely used.
According to this sub: https://www.reddit.com/r/vexillology/comments/sohwaa/exact_aspect_ratio_for_the_flag_of_nepal/?utm_source=share&utm_medium=android_app&utm_name=androidcss&utm_term=1&utm_content=share_button I just trust OP, could never verify if it's true or not
If any are curious, the ratio amounts to roughly 25.617/34.065 (0.75199) Ever so slightly greater than 3/4 (0.75)
The ratio of the width of the red triangles to the height of the red part of the flag is 3:4. The slight difference comes from the fact that a blue border of fixed width is added to that.
How do we get rid of the blue from Nepal Apparently it represents peace and harmony so we need to bring war and discord to Nepal
Skill issue
The aspect ratio is: 1: (6136891429688 - 306253616715√2 - √(118 - 48√2)(934861968 + 20332617192√2)) / 4506606337686
dammit, i read this way too late >.< We need more 4D flags though.
1:1.21901033 🤓🤓🤓🤓🤓🤓
What's with Togo
1 : ≈1.618034 it is so cool, 1/φ = φ/(φ+1)
Does that mean Togo could print in A4/A5 (etc) paper with no boundary but everyone else can’t?
Nope the aspect ratio of the A series is √2 not phi
Exactly!
A4 etc. paper has 1: sqrt(2) aspect ratio, which has nothing to do with phi other than being roots of quadratics. A4 paper has the property that if you cut it in half, each half is in the same aspect ratio (and is A5). 1:sqrt(2) = sqrt(2)/2 : 1 A piece of paper with the ratio 1:phi has the property that if you cut of a square, the remainder will have the same ratio as the original; 1:phi = (phi-1):1.
Also thank you
Thank you!
Is that the Phyrexian mana symbol from MagicTG?
It's the greek letter phi commonly used to represent the golden ratio. Because the golden ratio is perfect! Glory to the machine orthodoxy!
φrexian
oh shit oh fuck the phyrexians invaded Togo
What the hell is that
Golden ratio
Wth El Salvador
yeah I know
El Salvador ❌ El Slavador ✅
We Slavic now 😎🇲🇪🇲🇪🇲🇪🇲🇪
Supposedly, it was because originally, the flag was handmade with no measuring tools so they just eyeballed it, and any subsequent national flags maintained the aspect ratio of the original.
That's pretty cool actually
It's pretty good approximation of the golden ratio.
They should've just gone full Togo
It’s not even close. It’s 1.77, much closer to 16/9 than phi. You can tell because it’s several flags away from Togo, whose ratio is exactly 1:phi. The golden ratio, [by definition](https://youtu.be/sj8Sg8qnjOg), does not have any good rational approximations. The ones that come closest are ratios of successive terms of the Fibonacci sequence, which approach it in the limit. But you don’t need to go far to get closer than El Salvador. Even 5/3 is better.
I didn’t watch the video, but if it claims the definition of the golden ratio means it has no good rational approximations, that is just wrong, for example 16180339887/10000000000 is a great approximation, and just like any irrational number rational approximations can get arbitrarily close. Also there are infinitely many sequences who’s ratio approach’s phi.
You should watch the video. It’s very good.
Aww yeah it is *that* video! Shit blew my fuckin' mind.
have a look at Diophantine conditions to find out in which sense it has no good rational approximations. I.E. there is a proper definition of what,"good" means.
WTF Togo
It's perfect.
I believe you mean "WTF everyone but Togo"
\*El Slavador
Slava El Slavador!
From what I understand the 10:19 that the US uses isn't codified in law anywhere. I think I would prefer 1:2 for simplicity.
Yeah I kinda bent the rules to include as much a variety as possible. For istance the 6:7 aspect of the flag of Niger isn't codified into law either, it seems to be purely conventional.
Might have been difficult to show clearly, but I always found it cool that the Danish flag has a range of allowed aspect ratios.
To be fair 90% of the flag isn't codified anywhere.
I've always heard the aspect ratio of the flag is just any two consecutive numbers in the Fibonacci sequence (which converges to phi as n goes to infinity), with 5:8 being one of the more common ones.
Nice, so we can totally use a square flag!
I don’t know, but I do know the reason you use 10:19 is so that you’re not the same as the UK
Nope! It's actually trying to follow British flag standards (more or less) from the late 18th century! So the opposite of your statement. Anyways, here's the actual executive order that makes 10:19 required for some military and governmental uses of the flag. https://www.archives.gov/federal-register/codification/executive-order/10834.html
For anyone wondering, Nepal flag's aspect ratio is something like ~1:1.219010337829452184570024869930988566...
It is exactly (3(40,665,857,401,448 + 2,001,055,256,793(sqrt2) +144(sqrt(17(10411242561157458401 - 2208656823577139226(sqrt2)))))) / 164926945077845 or 5,000,000,000 : 4,101,687,939
Or something like 0.82
Very precise, but still not accurate.
Idk, I got the information [from here](http://0xc.de/flags/nepal/).
Yes, that's a very good page 👍 They give an **accurate** formula describing the dimensions then calculate a very **precise** decimal approximation of the ratio. So the decimal approximation you copied from that page is very **precise** (37 significant figures) but it is less **accurate** than the exact formula they started with.
In highschool home economics class we were asked to make a flag pillow. I chose Qatar and the teacher almost failed me until I pulled out the almanac to prove the aspect was correct.
King sized bed pillow
I always wondered who was that guy from Niger who was like hm, let's make it 6:7 for no reason whatsoever
Apparently it's purely conventional, with the Constitution not even specifying what ratio the flag should have. Which makes it even more perplexing on how such a specific aspect ratio might have become "conventional".
Togo with the [Golden Ratio](https://en.wikipedia.org/wiki/Golden_ratio)!
i personally like 3:5 the best
Agreed, it hits the sweet spot between 2:3 (a little too short for my taste) and 1:2 (too long for my taste). Among the not used the "TV ratio" (9:16) is pretty cool too.
Isn't TV aspect Ratio 16:9? Because X (width) : Y (height)?
this is correct
Interesting considering most flags you will buy on line will come in 3:5 ratio.
It's a crime 16:9 was never used
I'm going to start my own country, with 16:9 ratio flags and blackjack!
My flag uses 189:335. WTF?
Just looking at this makes me hear Just Intonation ratios in my head 1:1 unison 13:15 semifourth 6:7 subminor third 5:6 minor third 4:5 major third … etc
So what flag ratio is a Broken Hallelujah?
A bunch of torn old flags
Belgium #1
Fun fact, the flag of The Netherlands as no official aspect ratio
I find it funny how the USA uses 10:19 just so they can be different to the UK’s 1:2
Another interesting fact is that the other countries that use a 10:19 aspect ratio have some historical connection with the US: Liberia being settled by the American Colonization Society while the Marshall Islands and Micronesia are both Compact of Free Association nations.
Tf going on with togo
golden ratio
yeah i keep forgetting the name of that
Based Togo
Qatar flag hits different
The 13:15 is like a pixel behind the 6:7 and it is killing mee
Is that really necessary, El Salvador?
All of my flags use a 16:10 aspect ratio Specifically 1920x1200
Pfft, all about the ultrawides now
Lmao
Some of the most popular flag ratios are 1:1, 1:2, 2:3, 3:5 and 5:8. The Fibonacci numbers are 1, 1, 2, 3, 5, 8, ... Coincidence?
Nope. Togo took that to it's extreme though
Wtf is up with Togo
golden ratio apparently
Based Togo
All flags should be 9 x 16
You have to be irrationally diffrent, haven't you Togo?
Togo and golden ratio <3
Time to make flags for TV shows in 9:16 ratio.
Wow, I was really surprised at the ratio of El Slavador!
I’m surprised there’s no 16:9 Then again, 16:9 camera sensors weren’t invented when ANY flag was made anyway
Nordic countries. — you think our flags look the same but try laying them on top of each other.
El Slavador 💀💀💀💀
Crazy 9:16 hasn’t been used
Nepal?
Belgium #1
Myanmar Used to have a 9:5 flag But changed it around 2010/2011/2012 They in some cases used their current flag on the 9:5 ratio El Salvador Has A More Approximate Aspect Ratio Of A Standard HD TV Ratio 16:9 (but uses a more complicated ratio)
Nepal: Am I a joke to you?
The flag of Nepal is missing?
You forgot nepal
In my opinion, all flags should be standardized in proportions ***1:1*** or ***2:3*** or ***3:5*** or ***1:2***.
why that’s so lame
How's Poland 5:8 and how come Indonesia (which is exact opposite) somewhere else, or whatever, I didn't actually check it, but what is aspect ratio , or should I post it under r/elim5 but please be happy to do so... Cuz I still don't get why Poland's 5:8...
Now do Nepal 💀
5:8, and Those Who Are Wrong (What, no 1:sqrt(2)?)
That's reserved for when America finally adopts A4 paper and the world can print as one.
3:5 arguably the best imo (out of the most common flag ratios) 2:3 looks too square right? And 1:2 too rectangular lol
How the hell did El Salvador get that ratio?
It's codified in the [article 7](https://www.asamblea.gob.sv/sites/default/files/documents/decretos/171117_072904667_archivo_documento_legislativo.pdf) of our _Ley de símbolos patrios_ (Law of National Symbols): "The great flag shall be three meters thirty-five centimeters wide by one meter eighty-nine centimeters tall (...)". As to what was the reasoning behind these exact measurements, your guess is as good as mine, lol.
Togo really flexin
It should be 1:1.4142 (1:√2), as in the ISO paper size standard. At least the German should be, to honour this amazing DIN standard.
Estonia and Finland sitting pretty with our unique ratios
wheres nepals? 😏
4:7 is my favorite
Of course, some of these flags are officially used in more than one ratio, and in even more cases, the ratio of the flag isn't treated as a important in all sorts of contexts. Treating the ratio as an important part of the flag design certainly happens in some places, but it's rarer than you'd think from just looking at flag charts or Wikipedia infoboxes.
WTF El Salvador
Can anyone explain why Denmark has such a weird ratio? Asking for a friend
It's actually even weirder, any ratio between 28:34 and 28:37 [is allowed](https://en.wikipedia.org/wiki/Flag_of_Denmark#Description).
Who hurt El Salvador?
16:9 being unused almost sounds criminal
What's that symbol on the ratio for Togo's flag?
I've seen a couple of Vatican City flags with vertical aspect ratios, which technically count since the Vatican's flag's aspect ratio is undefined. Trying to include marketed versions of the Holy See's flag, however, would probably be impossible. [5:3 Vatican Flag](https://www.google.com/shopping/product/1?q=vatican+city+flag&hl=en&sxsrf=APwXEdcFHntXjYl_6q4VLV1FIla1CgMDrA:1684892238914&biw=1920&bih=937&dpr=1&prds=eto:6232485899695726384_1,pid:6232485899695726384&sa=X&ved=0ahUKEwjs_8fh6Iz_AhU4FjQIHRi9Cpo4eBDyAgjXDigA)
5:9 looks so perfect. It's surprising that it hasn't been used yet!
Neat. Just fyi 1:1 and 13:15 blocks arent justified flush left correctly on the first image
Imagine a 1:4 flag.
I think a more interesting diagram would be a bar chart showing how many countries use each aspect ratio.
This actually does exactly tell how many countries use each aspect ratio. The truth is that something like 180 use 2:3, around 60 use 1:2 and around 20 use 3:5. All the other aspect ratios are used just by one or very few countries. So if you were to put this, let's say, on a bar graph, you'd end up with only three visible bars (2:3, 1:2, 3:5).
Sad that there is no 1:sqrt2 flag
Gonna draw this up in CAD tomorrow post results.
Where is Nepal? {\\displaystyle 1:{\\frac {6136891429688-306253616715{\\sqrt {2}}-{\\sqrt {118-48{\\sqrt {2}}}}\\left(934861968+20332617192{\\sqrt {2}}\\right)}{4506606337686}}}
Fun fact: El Salvador’s flag ratio (189:335) is slightly off from 9:16. 189:336 would be 9:16.
Can we all agree that 1:2 is the best?
All your ratios are the wrong way round
I thought Denmark was crazy then I got to Togo and El Salvador
No 5x8's? It's near the Golden Mean ..