Posts tagged ‘flag’

The Amazing National Flag of Nepal

The National Flag of Nepal is unique.

Nepal Flag

Here are several trivia questions about the Nepalese flag:

  1. It is the only non-quadrilateral national flag in the world. What is its shape?
  2. It is one of only three national flags where the height is not less than the length. What are the other two?
  3. What is the sum of the three acute interior angles within the flag?

Question 3 may be difficult to answer without knowing more about the exact dimensions of the flag. For help with that, we turn to the Constitution of Nepal, promulgated 20 September 2015, which contains the following geometric description for the construction of the flag:

SCHEDULE – 1
The method of making the National Flag of Nepal

  1. Method of making the shape inside the border
    1. On the lower portion of a crimson cloth draw a line AB of the required length from left to right.
    2. From A draw a line AC perpendicular to AB making AC equal to AB plus one third AB. From AC mark off D making the line AD equal to line AB. Join B and D.
    3. From BD mark off E making BE equal to AB.
    4. Touching E draw a line FG, starting from the point F on line AC, parallel to AB to the right hand-side. Mark off FG equal to AB.
    5. Join C and G.

The traditionalist in me wishes that “line segment” were used instead of “line,” or that the overline were used to indicate those segments, and that a few more commas were inserted to make it more readable. Consequently, the math editor in me feels compelled to rewrite the directions as follows:

Nepal Flag Method Math

But the American in me — given how many times someone in the United States has tried to legislate the value of π — well, I’m just excited to see accurate mathematics within a government document.

The description continues for another 19 exhilarating steps, explaining how to construct a crescent moon in the top triangle, a twelve-pointed sun in the bottom triangle, and a border around the shape described above. Those steps are omitted here — because you surely get the gist from what’s above — but the following “explanation” that appears below the method is worthy of examination:

The lines HI, RS, FE, ED, JG, OQ, JK and UV are imaginary. Similarly, the external and internal circles of the sun and the other arcs except the crescent moon are also imaginary. These are not shown on the flag.

The entirety of this construction, as any classical geometrician would hope, can be completed with compass and straightedge. I cheated a bit and used Geometer’s SketchPad, with this being the resultant mess:

Nepal Flag Construction

Geometer’s SketchPad Construction of Nepalese Flag

The rough part was placing C so that AC = AB + 1/3 AB. Geometer’s SketchPad could have easily measured AB, calculated 4/3 of its length, and then constructed a “circle by center and radius,” but that felt like cheating. Instead, I…

  • located Q, which is halfway between A and D;
  • constructed circle A with radius AQ = AP;
  • constructed circle P with radius PD;
  • constructed circle D1 with radius DA;
  • located the intersections of circle P and circle D1 at points X and Y;
  • constructed a line through X and Y;
  • located R, which is 1/3 of the way from D to A;
  • constructed circle D2 with radius DR; and,
  • located C, so that CD = 1/3 AB.

Now, you could use that information to determine CF and FG, and then use the arctan function to calculate the measures of the two acute angles in the upper pennon. If you were so inclined, you’d find that their measures are 32.06° and 57.94°, respectively.

But the question above asked for the sum of the three angle measures. Without any work at all, it’s clear that the sum of those two angles must be 90°, since the construction described above implies that ΔCFG is a right triangle.

And because AB = AD by construction, then ΔDAB is an isosceles right triangle, and the measure of the third acute angle must be 45°.

And that brings us to a good point for revealing the answers to the three questions from above.

  1. Pentagon
  2. The flags of Switzerland and Vatican City are square, so the height and width are equal.
  3. 135°

If you’re looking for more flag-related fun, check out the MJ4MF post from Flag Day 2016 about converting each flag to a pie graph.

June 7, 2017 at 9:38 pm Leave a comment

Flag Day Math

Tuesday, June 14. Flag Day. It’s nearly impossible for mathy folks to not tell this joke today.

Several engineers were attempting to measure the height of a flag pole. They only had a measuring tape, and they were getting quite frustrated trying to slide the tape up the pole. They could get the tape no more than a third of the way up the pole before it would bend and fall down.

A mathematician asks what they’re doing, and they explain. The mathematician offers to help. She removes the pole from the ground, sets it down, and measures it easily. She then returns the measuring tape to the engineers, and walks off.

When she leaves, one engineer says to the others, “That’s just like a mathematician! We need to know the height, and she gives us the length!”

Those who know it will also tell this one, or a variant.

How do statisticians determine which banner to hoist?
They take a flag poll.

And then there are jokes about specific flags.

I’m about as motivated as the guy who designed the Japanese flag.

Japan Flag

Honestly, I want to stop. But I can’t. Just one more…

What’s the best thing about Switzerland?
I don’t know, but the flag’s a big plus.

Switzerland Flag

Okay, seriously… I didn’t invite you here today to listen to bad jokes. (Well, that’s not the only reason, anyway.)

I invited you here today to have a little Flag Day fun with math. The projectionist Shahee Ilya has converted the flag of every country into a pie graph based on its colors. For example, the Austrian flag has two red stripes and one white stripe, so it is converted to a pie graph as follows:

Austria Flag Hand Right Arrow Austria Pie Chart

Pretty cool, huh?

What follows are pie graphs for ten flags. Even if you are geographically challenged, I assure you that you’ve heard of all ten countries represented below. Can you name the country whose flag was used to create each pie graph?

Flag1 Flag2
Flag3 Flag4
Flag5 Flag6
Flag7 Flag8
Flag9 Flag10

 

Stumped by the challenge? Here’s a hint: The countries whose flags are represented above are the ten most populous countries on Earth. (Admittedly, had someone asked me to name the ten most populous countries prior to writing this post, I would have been lucky to identify half of them.)

And just to put some space between the pie graphs above and the countries whose flag they represent below (i.e., the answers), I include for your enjoyment one of the most hideous puns you’ll ever see, modified from an even worse version at Six Puns:

During a recent heat wave, a poll revealed that beads of sweat had amassed (mast) on the secretary’s forehead and a virus was rippling through the office staff. Although the boss knew that the secretary was very sick, he saw no reason to ban her from the office. Instead, he wrote a note with pennant (pen and) paper, and he flagged the issue to be addressed with the standard protocol.

If you tolerated that, you certainly deserve the answers…

Nigeria Pakistan
Russia United States
Indonesia Japan
Bangladesh Brazil
China India

 

Click on over to shaheeilyas.com/flags to see the pie graph for every country in the world. Clicking on the pie graph will reveal the flag and country name.

June 14, 2016 at 10:51 pm 1 comment


About MJ4MF

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

MJ4MF (offline version)

Math Jokes 4 Mathy Folks is available from Amazon, Borders, Barnes & Noble, NCTM, Robert D. Reed Publishers, and other purveyors of exceptional literature.

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