Flag of the United States specification
See "Flag of the United States" article for details.
The exact values are given in parenthesis, see graphics above, for the modern US flag with 50 stars. Older flags do not get adjusted for any reason.
- A = 1.000 = (1/1)
- B = 1.910 = (B/A = 1.910 fixed)
- C = 0.53846 = (7/13)
- D = 0.7615 = (C*sqrt(2) = 7*sqrt(2)/13)
- E = F = 0.053846 = (C/10 = 7/130)
- G = H = 0.06346 = (D/12 = 7*sqrt(2)/(12*13))
- K = 0.061803 = (inv(5x(sqrt(5)+1))
- L = 0.07692 = (1/13)
How is this obtained or calculated? See below:
Let, A = 1
A = 13L
L = 1/13 = 0.076923...
C = 7L = 7/13 = 0.5384615...
D = 0.76 (From "Flag of the United States" wiki article: B x 2/5 which is correct only for this AR of the flag, in fact, D/C looks to be about sqrt (2) and if so, then D = 7xsqrt(2)/13 = 0.7614996... )
Given: E = F, then E = F = C/10 = 7/130 = 0.05384615...
Given: G = H, then G = H = D/12 = 7xsqrt(2)/156 = 0.0634583...
K = 0.0616 (From "Flag of the United States" wiki article: L x 4/5 = 4/65) = 0.06153846... which contradicts what was given. The correct value for K is inv(5x(sqrt(5)+1)) = 0.061803398874... if we work this number backward we will get K = L x 4.017220926874.../5) and somebody rounded it off or over simplified it, there is where the confusion came from.
The aspect ratio, B/A, is independent of all other parameters and is stated as 1.9, but its rounded off from 1.91 (see the main "Flag of the United States" text for the 0.01 rounding error.)
B = 1.910
Just in case you wanted to make your own flag and all these numbers look too complicated, Here is something simple:
US Letter paper size is 8.5x11. Fold 1/2 inch to get 10.5 inches. Thats your "B" and you can get one flag out of a paper:
A = 5.5 inch (this is your height of the flag)
B = 10.5 inch
L = 27/64 inch (height of each stripe)
C = 2 15/16 inches or 7 stripes
D = 4 3/16 inch
E = F = 19/64 inch
G = H = 11/32 inch
K = 11/32 inch
Alternatively, fold 1/2 inch on the other side so you get 8 inches on one side. Thats your "B," and you can get two flags out of a paper:
A = 4 3/16 inch (this is your height of the flag)
B = 8.0 inch
L = 5/16 inch (height of each stripe)
C = 2 1/4 inches or 7 stripes
D = 3 3/16 inch
E = F = 7/32 inch
G = H = 1/4 inch
K = 1/4 inch
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