7) Patterns in Pascal’s triangle: There are a large number of patterns to discover – including the Fibonacci sequence.
8) Finding prime numbers: The search for prime numbers and the twin prime conjecture are some of the most important problems in mathematics.
12) Magic squares and cubes: Investigate magic tricks that use mathematics. 13) Loci and complex numbers 14) Egyptian fractions: Egyptian fractions can only have a numerator of 1 – which leads to some interesting patterns. Can all fractions with a numerator of 2 be written as 2 Egyptian fractions?
The authors of the latest Pearson Mathematics SL and HL books have come up with 200 ideas for students doing their maths explorations.
I have supplemented these with some more possible areas for investigation.
With a bit of ingenuity you can enrich even quite simple topics to bring in a range of mathematical skills.
Be aware that this page gets a large amount of traffic from IB students – do not simply copy articles – it may well be spotted by the moderators.
5) Diophantine equations: These are polynomials which have integer solutions.