IB Extended Essay: Math Research Topic Suggestion

[gsingh2011]

Hi, I need to write a 4000 word math research paper and I'm looking for a topic. Some sample topics that were given are,

Solving the problem: A piece of land of a square shape with dimensions 10m x 10m is divided into 100 square parcels with dimensions 1m x 1m. Initially, 9 of the parcels are overgrown by weed. If a parcel is surrounded by at least 2 parcels with weed from its sides after some time that parcel will be overgrown by weed. Can the whole piece of land grow into weed after some time?

Alhazen's Billiard Problem: on a circular table there are two balls; at what point along the circumference must one be aimed at for it to strike the other after rebounding off the edge.

The 3n+1 conjecture, where if you take a natural number n and apply n/2 if its even or 3n+1 if its odd, repeat the sequence, you will eventually reach one.

These are just some examples of past papers. I would like an interesting topic that would be fun to research. This is for my IB Extended Essay. If you don't know what that is, it is a 4000 word research paper I need to write in order to get my IB diploma (that's a high school diploma).

I'm curious to see what topics you guys suggest! Thanks.

 

[rhiansung14]

Why don't you try having a research paper that will discuss the digital value. Try to introduces a new idea of assigning every number a characteristic value. That would be great!

 

[Petr Mugver]

n ladybugs are initially on the vertices of a regular n-polygon of edge-length l. Each ladybug follows the next one with velocity v. After how much time will all the ladybugs meet at one point?

 

[desy.kris]

I'm doing IB too and I am thinking of doing Math too! :S