Below is a list of various computational and mathematical projects which I have completed in the past.
TSP project (WIP)
For my Computer Science coursework at school, I decided to do a program which takes a heuristic approach to solving travelling salesman problems, specifically applying it to sporting event calendars, such as Formula 1. Instead of just optimising for raw distance/time like most similar programs, this project would instead optimise for both emissions and financial cost, with the end user defining the weighting for this. The project will also not just consider direct flying distance between locations, but also potential road travel, which should help lower emissions. Finally, the calculated routes would be shown visually on a globe representation on a website.
Trebuchet mechanics research (WIP)
For my Physics PAG 12, which requires me to do independent research in a chosen field of Physics, I decided to do research behind the mechanics of a trebuchet. Whilst the maths behind this started relatively simple, once you start to add extra features to the trebuchet to make it more realistic the maths starts to get much harder. For example, if it is modelled with a fixed arm with the projectile and counterweight both directly attached to this, you can use Newtonian mechanics and some differentiation to generate formulae and optimise for the mass ratio; whereas if you modelled it with the projectile attached to a sling and the counterweight to a string, you have to use the much more complicated Lagrangian mechanics – which produces second order differential equations that you cannot solve analytically, and you must resort to numerical methods like Euler’s method or RK4.