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Mauritania - Construction Sheet

2:3 by Željko Heimer, 24 January 2018

Description
Updated description (2020)

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Mauritania

Description

The specification for the flag (provided by Embassy of Mauritania in Tokyo, Japan) gives the hoist as a 20/60/20 for the red/green/red areas. In the green section, the crescent and star take 67% percent of that space (20/10/40/10/20 according to the sheet). The other interesting thing is that the tip of the crescent horns end where the star arms meet at their outermost points. The flag maintains the 2x3 overall ratio.

There are also assigned colors; green is Pantone 354 Uncoated, Yellow as Pantone Yellow 012 Coated and Red as 18.1664. I believe the red shade is an error as Pantone does not have partial values; my guess is 186 Coated.
Zachary Harden, 24 January 2018

Everything except 20-10-40-10-20 and 75-75 are speculations based on the drawing provided in the specifications. The star seems to be set in a circle with radius 10 its bottom being in the centre of the flag (crossing point of the diagonals), thus its centre 10 units toward the top of the centre of the flag.
The horizontal line of the regular star inscribed in it (being approximately 13 units upwards from the horizontal median of the flag) seems to be also the line in which the horns of the crescent end.
The crescent itself seems to have been constructed not from regular circles, but ellipses, the lower edge being an ellipse with the centre in the above-mentioned horizontal line ca. 13 units up from the median, with axes being 74 and 66 (horizontal and vertical respectively). The upper edge is in an ellipse with the centre at the edge between the red and green fields, thus 30 units above the median, with axes 82 and 80. This makes the crescent at its widest 10 units wide.

Now, it may well happen that this speculation is not worth much, as the drawing we got may have been distorted in scanning and other procedures it went through, or it may simply be not precise drawing enough in those details, but this is best we have so far.
Željko Heimer, 24 January 2018

Updated description (2020)

2:3 by Željko Heimer, 24 January 2018

In May 2020: The government published http://www.kennach.gov.mr/documents, the graphic design manual. At http://www.kennach.gov.mr/IMG/pdf/_ar_fr_charte_graphique_mauritanie.pdf is a very detailed specification of the national flag (http://www.kennach.gov.mr/docs/plan01.pdf) usage guidelines, along with specifications of the national emblem.
Zachary Harden, 3 November 2020

The specification sheet provided is overzealously providing dimensions for the star construction, quite unnecessary, that obfuscate the more important construction details, but with a careful interpretation, it may be determined. So, here it is how I gather this. Also, some of the measures are obviously wrongly indicated - but the "true" meaning can be figured out.

The overall dimensions of the flag are 100:150 (for ease of number manipulation, the decimal free construction would simply take 10 times larger numbers). The width of red stripes is 20 units each, making the green stripe 60 units. The yellow emblem is set in the center of the flag in an imagined rectangle 75 units wide and 40 units high. This makes 37.5 units of horizontal space on each side from the vertical flag edges to the tips of the crescent, and 10 units from the top and bottom edges of the green stripe to the top of the star and the bottom of the crescent.

That was easy so far...

To match the (over)provided dimensions of the star, the diameter that I found mostly matching the prescriptions is 20.85. This may probably be easily approximated to 21 or even down to 20 units without much practical difference - since no other dimension depends on it. Of course, the top of the imaginary circle circumscribing the star matches the center of the top edge of the imaginary rectangle containing the yellow symbols, and the star is a regular five-pointed star made of diagonals connecting every second vertex of the inscribed pentagram (as usual).

The arches forming the crescent are tricky - consisting of ellipses. The center, designated C1 on my drawing, of the ellipse forming the bottom arc of the crescent is set, according to the provided prescription, 3.5 units beneath the top of the star. The longer horizontal semi-axis equals 37.5 units (so to make 75 units overall dimension of the rectangle, thus tangent to the vertical edges of that rectangle), while the vertical semi-axis is 36.5, also tangent to the edge of the imaginary rectangle. This makes the ellipse that reaches the top at 3 units outside the flag surface above the center of the top edge of the flag.

The requirement for the top arc of the crescent is to intersect the first arc at the furthest points, i.e. where they are tangent to the imaginary rectangle along the main axis of the first ellipse. Also, it is required that the vertical width of the crescent at the widest is 10.2 units. Not using mathematically precise construction (which may yield slightly more precise dimensions, but not necessary for any practical purpose), this is achieved with an ellipse with the center, designated C2, 5.1 units above the center of the first ellipse, and with the semi-axes A2 38 units and B2 31.4 units. The top of this ellipse tangents the first ellipse, i.e. they are at the same point outside the flag surface.

And that provides for the complete flag construction. I provide the "standard" FOTW gif and a larger image with details of the construction better visible.

dr. sc. Željko Heimer, 3 November 2020