The Bernoulli Quadrisection Problem requires us to divide the area of a given triangle into four equal areas using two perpendicular straight lines. One of the areas must be a triangle, and the other three must be quadrilaterals. We have solved this old, but difficult problem using Particle Swarm Optimisation (PSO), an algorithm that was devised in 1995. We also used PSO to solve a very modern problem arising in the design of electronic circuits using Very Large Scale Integration (VLSI). Our solution of this VLSI problem required us to develop a modified PSO algorithm involving the use of multiple particle swarms. This experience encouraged us to develop a number of new, very efficient particle swarm algorithms.