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Dimensional comparison of the Southern Crosses on five national flags

Dimensional comparison of the Southern Crosses on five national flags
Country First adopted Adopted as national flag Number of stars Colour of stars Sizes of stars* (Alpha Crux = 100)

Australia 1902 1954 5 white 100 : 100 : 100 : 100 : 58

Brazil 1889 1889 5 white 100 : 83? : 83? : 66? : 46?

NZ 1869 1902 4 red, with
white fimbriation 100 : 85 5/7 : 85 5/7 : 71 3/7 : ---

PNG 1971 1975 5 white 100 : 100 : 100 : 100 : 50

Samoa 1948 1962 5 white 100 : 80 : 80 : 75 : 50

Dimensional comparison of the Southern Crosses on five national flags
Country	First adopted	Adopted as national flag	Number of stars	Colour of stars	Sizes of stars* (Alpha Crux = 100)
Australia	1902	1954	5	white	100	:	100	:	100	:	100	:	58
Brazil	1889	1889	5	white	100	:	83?	:	83?	:	66?	:	46?
NZ	1869	1902	4	red, with white fimbriation	100	:	85 5/7	:	85 5/7	:	71 3/7	:	---
PNG	1971	1975	5	white	100	:	100	:	100	:	100	:	50
Samoa	1948	1962	5	white	100	:	80	:	80	:	75	:	50

Country	Number of points*	Angle of limbs	Height	:	Angled width	:	Horizontal width**	Proportional lengths of arms***
Australia	7:7:7:7:5	81.964°	100	:	71.536	:	70.833	1	:	0.586	:	0.546	:	0.521
Brazil	5:5:5:5:5	****			****					****
NZ	5:5:5:5:-	82°	100	:	72.222	:	71.517	1	:	0.583	:	0.5	:	0.5
PNG	5:5:5:5:5	87.397°	100	:	66.736	:	66.667	1	:	0.565	:	0.692	:	0.565
Samoa	5:5:5:5:5	85.470°	100	:	90.950	:	90.667	1	:	0.672	:	0.495	:	0.688

* Alpha : Beta : Gamma : Delta : Epsilon Crux
** Height measures the vertical distance between the centres of Alpha and Gamma Crux, which stars are aligned vertically on all four flags. Angled width is the direct distance between the centres of Beta and Delta Crux. Horizontal width is the horizontal distance between these star's centres. The horizontal width is the angled width multiplied by the sine of the angle between the limbs. Measurements proportional for each flag given Height = 100.
*** Measures the straight-line length of the four arms of the cross, from the imaginary intersection of the limbs to each star's centre. Note that only on the PNG flag are the two arms of the short limb the same length. Order given is Alpha : Beta : Gamma : Delta Crux. Measurements proportional for each flag, given length of Alpha arm = 1.
**** It is not known whether Brazil's flag has been defined in enough detail to calculate these measurements.
Brendan Whyte, 25 January 2007

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