Have you got a Super Brain? Adapting and exploring maths challenge problems is an excellent way of finding ideas for IB maths explorations and extended essays. This problem is taken from the book: The first 25 years of the Superbrain challenges. I’m going to see how many different ways I can solve it. The problem […]

Fourteen IB Higher Level Paper 3 Practice Questions With the new syllabus just started for IB Mathematics we currently don’t have many practice papers to properly prepare for the Paper 3 Higher Level exam. As a result I’ve put together 14 full investigation questions – each one designed to last around 1 hour, and totaling […]

3D Printing with Desmos: Stewie Griffin Using Desmos or Geogebra to design a picture or pattern is quite a nice exploration topic – but here’s an idea to make your investigation stand out from the crowd – how about converting your image to a 3D printed design? Step 1 Create an image on Desmos or […]

Complex Numbers as Matrices – Euler’s Identity Euler’s Identity below is regarded as one of the most beautiful equations in mathematics as it combines five of the most important constants in mathematics: I’m going to explore whether we can still see this relationship hold when we represent complex numbers as matrices. Complex Numbers as Matrices […]

Sierpinski Triangle: A picture of infinity This pattern of a Sierpinski triangle pictured above was generated by a simple iterative program. I made it by modifying the code previously used to plot the Barnsley Fern. You can run the code I used on repl.it. What we are seeing is the result of 30,000 iterations of a simple […]

Sphere packing problem: Pyramid design Sphere packing problems are a maths problems which have been considered over many centuries – they concern the optimal way of packing spheres so that the wasted space is minimised. You can achieve an average packing density of around 74% when you stack many spheres together, but today I want to […]