# Rectangular representation (ignore the nonsense)

As the title says, ignore the nonsense, there's quite a lot of it too. Try look beyond the nonsense and give me the answer which is an image.

Hint 1

What four letter word might be represented by a rectangle?

This is the national flag of the Philippines.

The four boxes

The hint asks which four letter word could be represented by a rectangle. Flags are usually rectangles and besides their design, their aspect ratio is an important characteristic. The ratio 2:1 is a very common aspect ratio of flags.

So the letters F, L, A and G go into the four boxes.

The nonsese ignored

The "nonsense" is everything except F, L, A and G. Let's look at these particular boxes.

F: The radius of the circle is $$\frac{\sqrt{5}}{2}$$. The area of the red rectangle is then $$\frac{1 + \sqrt{5}}{2}$$. This is the golden ratio, phi.

L: I didn't know what to make of this at first. It was the last part I found and I found it by backwards solving: Each of the vertical stripes represents one letter of the word "ellipse". The red stripes spell lip.

A: The area of a circle with radius 1 is pi.

G: The inverses of the factorials sum to e. What do the arrows to the left and right mean? Well, the point north and south. This three-part-rebus reads nes.

What's the word? Phi lip pi nes.

Wrong paths taken

I was pretty sure that we were looking for a flag early on, but the ones I considered were those of countries whose names have four letters: Cuba, Fiji, Niue and perhaps Ireland (Eire). All letters of FIJI are there, for example, but the I occurs twice.

I also thought the the "nonsense" was something that is not rational, so that the answers that involved irrational real numbers like π, e or many square roots should be ignored. For example, the area of the triangle at D is 6 square units and the sixth letter is F. Everything points to Fiji again.

Of course, that got me nowhere. Then I saw the hint and thought: Meh, I know what kind of image goes into the rectange, I just don't know how to get there.

But the hint was useful, after all: It told me that I was going about things in the wrong order. (Putting the cart before the horse is the technical term, I believe.) I thought the first step was to find out what the nonsense was, but the first step was to fill the four boxes. Click!

• A lot of nonsense indeed, but this is it, nice job! :) Commented Jul 15 at 9:51