I need to write a paper for school on something, pretty much anything, to do with maths (could be stats) but i have no idea where to start. Is there anything cool / interesting you know of? Examples of past ones are 'modelling tumour growth', 'symmetry of spider webs' - that kinda thing
How about the Ulam spiral? And by extension, prime number theory in general?
If you haven’t heard of the Ulam spiral, check it out: if you write down sequential integers, starting from ANY NUMBER, in the shape of a spiral traveling outwards, and then circle all the primes, this (when you zoom out far enough) is what you get:
As you can see, there’s an obvious pattern of parallel lines. Nobody really understands why there’s this apparent ‘superstructure’ of primes (which you can see via other methods as well; the Ulam spiral is only the most famous). There are lots of proofs and theories that try to get to the bottom of it, though. And writing about primes means writing about cryptography, which is baller.