Mathematics Essay Topics

I have to write a 1500 word essay. It can be anything related to mathematics. E.g. optimization, rubix cube etc.
Can you please help me with some topics I can write on ?

Thanks in advance

Personally, I would investigate the Golden Ratio.
http://en.wikipedia.org/wiki/Golden_rati…

Call your essay topic "Applications and observation of the Golden Ratio" or something of that nature. I think you'll find it highly interesting. I've seen whole books on it and it's great fun.

There are applications and observations in...
Aesthetics
Architecture
Painting
Book design
Perceptual studies
Music
Industrial design
Nature
Optimization
Finance

Alternatively, call it "The Golden Ratio and the Fibonacci Sequence". There are highly interesting relationships such as the Fibonacci spiral, but you can cover these as well in the previous essay idea.

Alternatively, you could do something like "Pi through the ages", and look at Pi's discovery and the difference approximations and such.

How old are you?

I would always go with the Mobius loop. Its a loop of paper with a twist in it. When you cut it in half you just get one big loop. If it had two twists in it you get two interlinked loops. If you wikipedia this you can research this phenomenom and explain it in your essay. It should be more interesting than a standard mathematics essay too :)

probability would be fun....