Nautical stars look good both due to geometric appeal and because they just look cool in regards to modern aesthetics for whatever reason. I would not want one because I am super picky about what I wear and don't like things other people have. As per above, I've never heard anyone extolling their virtues. Usually people are just like 'hey those look pretty cool' and they do, in fact, look pretty cool.
..13, 21, 34, 55, 89...
One of the cooler applications of the golden ratio is converting miles and kilometers! It approximates the ratio, so say you have 30km and want it in miles, then just compose 30 as a sum of fibonaccis (don't be scared by math, it's easy!) and write it as, say, 21 + 8 + 1 then decrease each number once to get 13 + 5 + 1 = 19 miles. If you had thirty miles, go up one and get 34 + 13 + 1 = 48km. The higher the fibonacci number you use the better, and try to avoid using one because it is unreliable.
P.S. I am presently wearing the t-shirt I got from going to a math conference at which I learned that fibonacci trick... It is a friday night and I am drinking a beer and eating birthday cake alone at home.
