Research ideas for a 16 year old in mathematics and computer science?

[geekkid]

First of all, hello everyone, this is my first post to this forum, although I've been visiting it on a daily basis for a few months already, without an account.
I'm a 16 year old high school sophmore, and I'm required to complete a research project in 7 months from now. I'm very interested in mathematics, computer science so i thought i'd like to do my research in one or the other, but the problem is that i can't come up with an idea. What is there to research for a 16 year old in those subjects. I mean, I't seems quite unlikely that i could make a mathematical hypothesis and then write a proof for it orsth.
So my question is: have you got any research ideas i could do ?

PS: I've a hard time expressing myself in English because English is not my native language, so I'm sorry if you don't quite understand my post.
Thank You !

 

[micromass]

What do they expect of you?

Do they expect that you come up with a novel new idea and proof it?? That would be quite hard.

Do they expect that you study a theory, make some exercises, apply the theory and then make some exercises on it?

An idea is to study projective geometry. This is a very elegant mathematical theory and it's useful in computer science (graphics and stuff).

Spherical trigonometry is also quite nice. Maybe you can use that to build some kind of model for the Earth in your computer?? You might also want to find the diameter of the Earth using simple materials.

Studying conic sections is also quite nice. It has a lot of applications. For example, you can use it to build a parabolic mirror that lights something on fire. (maybe this is too farfetched...)

Maybe you can do something more programming related: build a traffic simulator on pc? Or simulate the solar system??