Flag Saga Part 3: More Timor or Vexing Vexillology
This is Part 3 of a series that I’m calling the Flag Saga. You should read Part 1 and Part 2 first if you haven’t already.
Assuming you’re all caught up, here is Part 3 of the Flag Saga:
Looking at the problematic United Nations Transitional Authority for East Timor (UNTAET) construction sheet for the East Timor flag and frustrated by the fact that there appear to be many differing versions of the East Timor flag on the internet, I decided to go to the East Timor government's website to see which version they list as the official flag.
Incorrect version of the East Timor flag from their own government’s website.
What I found was puzzling. The website uses what I can only describe as the most incorrect version of the flag that I have seen thus far. Not only is the black triangle the wrong size, but the white star is skewed and distorted and the colors do not at all match the Pantone Matching System (PMS) colors that are specified for the flag.
I traced the source of that troublesome image to a file that was sent via email in an attached word document on the night before East Timor's independence in 2002 by Dr. Andrew Leith who at the time was the Civilian Chief of Protocol for UNTAET working at the UN Department of Peacekeeping Operations.
Given the violence and turmoil surrounding the independence of East Timor and Andrew Leith's lack of vexillological or graphic design expertise, the inaccurate flag picture is pretty understandable. What's perplexing is that there doesn't seem to have been any official clarity brought to the issue in the 18 years since.
In order to try to rectify the situation, I created a new construction sheet from scratch (two versions of which are pictured here, one with sizes in centimeters and the other with ratios based on a flag length of unit size 1) based on what I thought was the best interpretation of the intent of the flag design. I sized the black triangle correctly, used the specified PMS colors, and rotated the star so that it pointed to the upper left corner of the flag as originally intended.
My rebuild of the East Timor flag construction sheet with measurements expressed as cm.
My rebuild of the East Timor flag construction sheet with measurements expressed as ratios relative to the total flag length.
I also changed the scale of the star. The original construction sheet specified that the length of the flag should be 180 cm and the diameter of a theoretical circle circumscribed around the star should be 29 cm. I found this rather strange since 29/180 is an inelegant and irreducible fraction but it is nearly imperceptibly different from a star that sits inside a circle of diameter 30 cm. Unlike 29/180, 30/180 reduces beautifully to 1/6. I don't know who I need to talk to in the East Timorese government to get that minor change in scale (along with clear and complete specifications for the rest of the flag) implemented but I think it's a good idea.
It turns out that I wasn't the first to make these corrections. The version of the flag on Wikipedia has the correct colors, size of the black triangle, orientation of the star, and the person who created it even made the same change to the scale of the star.
I did end up finding another version of a construction sheet on a vexellological website which I thought was equivalent to the construction sheet that I had just produced but when I showed it to my wife she noticed that there was a slight difference.
The Constitution of the Democratic Republic of Timor Leste specifies that: "In the centre of the black triangle there is a white star of five ends [...]". In Euclidean geometry the "center" of a triangle can be defined many ways including centroid, circumcenter, incenter, and orthocenter.
When I created my construction sheet, I interpreted the word center to mean incenter (the center of a circle inscribed within the triangle). This made the most sense to me for two reasons. The first is that it seemed most likely to result in an aesthetically pleasing image given an arbitrarily sized black triangle. The second is because the size of the star was defined by a circumscribed circle so it made sense to me to place it at the "center" of the triangle using an inscribed circle.
What my wife had noticed was that the other "good" construction sheet that I found online had used the centroid of the triangle (the arithmetic mean of all of the points within the triangle). While this definition of center also works aesthetically for this flag (the centroid of this particular triangle is in fact very close to its incenter), I would argue that using the incenter is a better idea because it works better for more differently sized triangles whereas if you use the centroid definition and start changing the dimensions of the triangle you very quickly run into cases where the centroid doesn't "feel" like the visual center of the triangle.
My wife doesn't share my opinion that the incenter is the best definition in this case. For triangles, the centroid also has the feature that if you draw a line from a triangle's vertex through the centroid, it will perfectly bisect the opposite edge of the triangle. She argues that because this whole East Timor flag kerfuffle started with ambiguity about the orientation of the star and since placing the star at the triangle's centroid results in a line that runs from the top left corner of the flag, bisecting one of the points of the star, travelling through the center of the star and perfectly bisecting one of the sides of the triangle, that is the more elegant definition in this case. This is of course a matter of opinion and technically either of the definitions would be perfectly valid for this flag. (In support of my wife's preferred definition, I will say that the flag is easier to construct geometrically using the centroid than it is using the incenter. Note: In marital disputes its important to try to see things from your partner's point of view.)
When I looked more closely at versions of the flag that are on the internet, some used the centroid while others used the incenter.
In the end, I think this is a great demonstration of why its important to be accurate and precise. After all this, I am still not exactly sure what the flag of East Timor is supposed to look like but I'm beginning to think that perhaps no one is.
Bonus: When one of my friends read Part 2 of the Flag Saga, she commented that she wanted to use my flag musings as math problems for her kids. Inspired by that idea, my wife and I decided to list a few questions that perhaps they (and anyone else interested) can try to solve. Those questions can be found here.