High School Applications of Morley's Theorem

[Cheesycheese213]

I was planning to do an essay exploring Morley's Trisector Theorem, but I was having trouble finding and real life applications of it?

It states that "in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle".

I thought it was pretty interesting so I chose it, but after researching it more, it looks like there really isn't much use for it other than being one of those "beautiful results" that are just interesting but can't really be used? One of the criteria is to reflect on the essay and what we learned, and we were told that we could for example relate it to the real world. But, if I can't even apply it to math I'm not very sure how I could do that?

Is there something (real life or in math) that the theorem can be applied to? Thanks!

 

[fresh_42]

This is as with many geometric theorems. They appear as rather abstract and useless, but surprisingly appear from time to time. If you asked me for an application of Thales, I would have to admit, that I don't know one. Nevertheless I used it very often and I'm sure, e.g. construction engineers use it, too. One thing that came to mind were snow chains. I don't know which underlying principles they use for manufacturing them, but I could imagine that Morley could be used in some force diagrams.

You could have chosen worse:
https://www.emis.de/journals/BAG/vol.43/no.2/b43h2sta.pdf
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.38.4801&rep=rep1&type=pdf
but Pythagoras, Thales, sine and cosine theorems are certainly the frontrunners of all geometric theorems with respect to their applications.