Last modified: 2005-08-11 by phil nelson
Keywords: ratio of flags | flag ratios | naval ensign | off-centered | scandinavian cross | golden section |
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My "holy book" (Whitney Smith, Flags Through the Ages and Across
the World) quotes for the United States' flags a 10:19 ratio, really closer to
the 1:2 traditional ratio of the British flags, from which the "Star
Spangled Banner" comes.
In fact there are three main "threads" in the world of flags:
British flags have a 1:2 ratio (United Kingdom, Australia, Bahamas, Canada, Ireland and with the little correction of 10:19 United States and of course Liberia);
French flags have a 2:3 ratio (France, Italy, Cameroon, Ivory Coast, Algeria, Spain and the most of Latin-American flags);
German flags have a 3:5 ratio;
Moreover some nations have unusual ratios, as Denmark
(28:37) or Belgium (13:15).
Alessio Bragadini
The British ensigns (including the Union Jack) ratio varied with the standard breadth of the textile industry, but always retaining a length of 18:
| Year | Ratio of Length to Breadth |
|---|---|
| 1687-17xx | 11:18 |
| 17xx-1837 | 10:18 (5:9) |
| 1837-present | 9:18 (1:2) |
On the other hand, I'm not sure how strict this regulations would be followed in civilian rebellions taking place in faraway Australia, nor how fast they were enforced throughout the empire...
I don't know at what point after 1837 the proportions were actually
regulated. Possibly not until the reorganisation of Squadron colours in 1864.
David Prothero, 03 June 1999
Many flags, picture frames, book covers, etc., are proportioned in
accordance with what artists and mathematicians call "the golden
section." This relationship exists when the length and width of a
rectangle are divided into extreme and mean ratio, or when the parts follow
(or approximate) the formula:
Another way to look at it is if the length and width roughly equal 62 and
38 percent of their sum respectively.
Lou Stewart, 1998 January 30
If you solve the equation Lou Stewart gave analytically,
you'll find a solution:
where:
Mathematically, there's another solution to this equation, namely
but I don't think we're looking for a flag with a negative length.
So, the ratio is 1.618...:1.
This ratio was already known to the Greeks, and the Acropolis reflects this
ratio in many ways (correct me if I'm wrong).
Filip Van Laenan, 1998 January 30
Let's try it this way:
the first format to think of is 1:1 (A:B), then we put the B as a new A, and
A+B as a new B. So next we'll get 1:2, and next 2:3 and 3:5 and 5:8 and 8:13
and 13:21 and 21:34 and 34:55 and 55:89 and so on... We'll get closer and
closer to 1.618 or something like that, the golden section. It has been used a
lot in art and Kepler spoke of 'divina proportio'. It is mostly a proportion
that 'looks nice'. Many mathematicians and physicists have written about it.
Ole Andersen, 1998 January 30
1.1618... is phi the golden ratio and is, like pi,
irrational. However, if we look at the Fibonacci series we'll see that the
difference between each number gets closer and closer to the ratio first over
then under. The series is 1 1 2 3 5 8 13 21 ... where each number is the sum of
the previous two. You will also note that the numbers are not far from many flag
ratios 5:8 8:13 13:21 etc.
Rich Hansen, 1998 January 30
A more interesting approach uses the Golden Ratio's connection to the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13,..., in which each new member of the sequence is the sum of the preceding two. Then, you can generate successive (and closer) approximations to the Golden Ratio as 1/1, 2/1, 3/2, 5/3, 8/5, 13/8,... where the numerator is just the member of the sequence that is one ahead of the denominator. (The two approximations above are derived from this method, just a bit further along in the sequence).
An awful lot has been written about the Golden Ratio (also called 'The Divine Proportion'). It crops up in nature: shapes of shells, arrangements of sunflower seeds; in architecture (the most aesthetic shapes are ones having proportions equal to the Golden Ratio), and flags! It was known to the Ancient Greeks (look at a picture of the Parthenon), and probably earlier. Interesting it should show up in flag design too!
anonymous, 1999 February 03At least one flag used the "golden
proportions" as an integral part of its design:.
Dave Martucci, 1998 January 30
No. There wasn't such flag manufactured in
Saarland. I don't know where the document which mentioned this was to be found,
but all the projects of laws of 1947 mentioned a flag with the proportions 1 x
1,5, not 1 x 1,61803398875. If such flag was proposed in Saarland, this was
really absurd and ridiculous: how can you draw precisely such a flag, and above
all how can you manufacture such a flag: it is impossible and not practical! If
the flag existed it was only a proposition, not a real flag.
Pascal Vagnat, 1999 February 05
New Brunswick's isn't a
national flag, but its 5:8 ratio is the closest approximation you can get to the
golden ratio with one-digit numbers. The designer probably considered this when
choosing the ratio. Any other flags with this ratio were probably designed with
the golden ratio in mind.
Dean Tiegs, 1999 February 05
Artists Bruno Tuukkanen and Eero Snellman had the
Golden Ratio in their mind when they designed the Finnish
flag. Ratio 11:18 = 0.6111... which differs very little from 0.6180...
Ossi Raivio, 1999 February 06
The proportions of vertical stripes on French naval flag are 30:33:37, to enable good visual effect
of flag when flying. Portugal, too, obviously, has an
off-centered pattern and I suppose the Scandinavian cross flags have the same
reason for the vertical bar shifted right.
Zeljko Heimer, 1995 September 23
Bangladesh, North
Korea, Nauru, Turkey and the Japanese Ensign all shift their designs to the hoist. Whitney
Smith's book mentions that Bangladesh does this so that the flag will look
proper while flying. There is no reason given for the others and in the case of
Nauru especially I suspect that the star is toward the hoist for some other
reason.
Nathan Augustine, 1995 September 27
Since we are talking about flag proportions, I was wondering if the
proportions are ever symbolic in and of themselves, or always more or less
arbitrary. (Let's leave oddballs like Nepal and Qatar out for the moment.)
This question arises from the question of why it's so important to keep the
proportions right. For instance, Ron pointed out that many of the errors are
caused by standardizations of the flag manufacturing process. Earlier, someone
said that all the flags of the former Soviet Union kept to the proportions of
the old Hammer and Sickle. Similarly, looking at my flag chart, all the flags
of the former Yugoslavia seem to be more or less the same proportions. I'm
willing to bet that this is a result less of nostalgia for the old days and
more of the fact that it was easier to leave the settings on the flag-making
machines as is....
Thus, I ask again, why is it important to keep proportions straight? Colors
and symbols have meanings which it would wrong to alter, but if proportions
are chosen arbitrarily...
Josh Fruhlinger, 1996 January 29
One pair of flags that differ only in their proportions are those of Indonesia (2:3) and Monaco (4:5). Of course, I don't know whether the proportions have significance in themselves, but they have significance in relation to each other in that they are the only way to distinguish the two flags.
I'm having a hard time thinking of a real-world situation in which these
two countries' flags could be confused, though. (Shipwrecked sailors wash up
on an unfamiliar shore; "What country are we in?" "Must be
Indonesia -- look at that flag." "Yes, and that big building up
there must be the famous Djakarta Casino!")
Bruce Tindall, 1996 January 29