Golden Ratio in Geometry

[Robocrow]

Hello! This is my first post here.

So I am planning on doing an extended essay in mathematics. I was originally planning on researching the Fibonacci sequence, but I've gotten a bit less interested in that and more interested in the golden ratio(phi) which can be derived from that sequence. I believe this would fit under the idea of "the beauty of mathematics" as written in the IB extended essay handbook for math.

I'm just having a little bit of trouble deciding exactly what I should focus on in my extended essay (and what would be to broad or too narrow). Right now my idea is to write it on how the golden ratio appears in geometry.

The smaller points I have under this topic that that interest me are

1. Phi appearing and being calculated using simple geometric problems/situations with 2D or 3D shapes

2. Phi's inherent link to the number five and its appearances in pentagons, penrose tilings, quasicrystals, and other things related to five-fold symmetry

3. How the shapes and patterns associated with phi are beautiful in nature, like the ancient arabic five-fold tilings and the golden rectangle in ancient (greek) architecture

I haven't done a TON of research yet, but this is what has stuck out to me so far. Is this too narrow or too broad of a topic? And does it fall under the guidelines for a math EE?

[Elizabeth O'Donnell]

I think that just focusing on the golden ratio in geometry is to broad, because there are so many different ways to see this. I think that your "smaller points" are a topic within themselves. I had the same problem as you when I began my EE I wanted to do it on forensic psychology, then had to narrow it down to the accuracy of offender profiling when identifying a suspect. I personally like number 3 on your list. Also I looked over the requirements for a math paper and it seems like your good. If you don't have it then here is a link to the requirements and criteria for all areas. Math is on page 96.

http://www.fcps.edu/RobinsonSS/ib/pdf/Extended%20Essay%20Subject%20Guidelines.pdf

[Robocrow]

Thanks! As for the #3, I feel like it is the hardest for me because it seems to have the least to do with the ratio itself, and more with our perception of what it creates. And I'm not sure how I would write a whole essay about that.