Partitions of Numbers

[Othko97]

As someone who loves maths, I am involved in what is known as Maths Working Group in my college. Last week we were told to make a presentation on either Partitions or this other problem which is similar, which I'll come to later.

Basically a partition is how many different ways can you make up a natural number from summing other natural numbers, so 3 has partitions (1+1+1),(2+1),(3). We were basically told to do stuff with them, so I did.

The other problem was to do with bubbles, and nesting them. So say you have 3 bubbles, how many different ways can they be arranged - you could have all three nested, 2 nested with one outside or all three not nested. Again we were just told to play around with this problem. Thoughts?

I'll attach my powerpoint as a word document and a program which finds the first n partitions (where you enter n), and saves your previous runs to a file, called Previous Runs. It's a java file, so tell me if you have problems.

[Pentagathus]

As someone who loves maths,

Aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaarrrrrrrrrrrrrrrrrrrrrrrrrrghhhhh!

[Glaurung]

Interesting - thanks for posting this. I played with this briefly, and then decided to read about it instead. Hopefully the Wikipedia article (http://en.wikipedia.org/wiki/Partition_(number_theory)) is all true.

Two particular points that surprised me:

• There's no recurrence formula for getting a partition number simply from the previous one or previous several.
• This area is related to pentagonal numbers (1, 5, 12, ...)

[Othko97]

Yeah, this was one of my favourite things we did last year While I don't think my method for solving either problem was particularly interesting, I found the problem fun! The pentagonal thing surprised me when I first saw it as well, which was shortly after the problem was set. By the way, wikipedia tends to be accurate for maths and sciences, however less so for more artsy subjects.

[Jubal]

Don't get me started on some of Wikipedia's history content.

[Cuddly Khan]

So Jubal, tell us all about Wikipedia's history content.