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

 

[CellCoree]

I would suggest exploring the applications of graph theory in real-world scenarios. Graph theory is a branch of mathematics that deals with the study of graphs, which are used to model relationships and connections between objects. Some possible research topics in this area could include:

1. The use of graph theory in social networks: You could explore how graph theory can be used to analyze and understand social networks, such as friendships, online interactions, and information dissemination.

2. Optimal routing in transportation networks: This topic could involve using graph theory to find the most efficient routes for transportation networks, such as road networks or airline routes.

3. Modeling disease spread using graph theory: With the recent COVID-19 pandemic, there has been a lot of interest in using graph theory to model the spread of diseases and predict their impact. You could explore different graph models and their effectiveness in predicting disease spread.

4. The traveling salesman problem: This classic problem in graph theory involves finding the shortest route that visits a set of given locations. You could explore different algorithms for solving this problem and their real-world applications.

5. The application of graph theory in computer science: Graph theory has numerous applications in computer science, such as in data structures, algorithms, and network analysis. You could delve into specific applications and their significance.

Overall, exploring the applications of graph theory in different fields can be an interesting and relevant topic for your extended essay. It will also allow you to develop your research skills and gain a deeper understanding of this important branch of mathematics.