Help Math Geniuses!!!!!!!?

Question

I need to research a certain topic for mathematics. It's not simply looking in books and internet, but I actually have to do the research. For instance, I heard one person last year used the golden ratio and researched if it affected sense of taste. They applied the golden ratio and made cookies and got people to judge whether the golden ratio cookies tasted better than the normal recipie cookies. This is a two year project so I would like an entertaining and informative topic.
P.S. My grade level is 10th grade but I'm looking for topics that are in the 11th-12th grade level.

Thank you

No Brenmore

Note: it doesn't have to be on the golden ratio and it has to be something that I could actually research deep into (meaning not a 1 sentence answer but a long answer 10+pages mayb?)

Answer 1

Why don't you use the golden ratio and make pan-cakes.

Answer 2

Well, if you want to do something on the golden ratio, some say that it influences the stock market. You could research that, and draw your own conclusion.

Or you could do something on the number zero. The history, the weird nature of it, etc... By the way, did you know that "The Babylonians invented it, the Greeks banned it, the Hindus worshipped it, and the Christian Church used it to fend off heretics. Today it's a timebomb ticking in the heart of astrophysics." Quoted from "Zero: The biography of a dangerous idea" By Charles Seife.

Or do something on the square root of negative one, though it may be very challenging...

For the Golden Ratio, you could also research how it affects nature, like with the seashells and stuff.

Oh, yeah, and another one: the Fibonacci numbers. It may be a little simple, but you could research how it is found in nature.

Some good books on the subject:

The Golden Ratio, by Mario Livio
The Story of (square root of negative one, in its mathematical form) by Paul J. Nahin

Zero: The Biography of a Dangerous Idea by Charles Seife

*edit*
You could also research string theory, or quantum mechanics, if you don't want to do the golden ratio. The string theory is rather fun and interesting.