The Travelling Salesman

Ontario has 413 uniquely named municipalities comprising 99.3% of its total population of 13,448,494 (2016). Suppose you wanted to visit each of them in your jet-powered helicopter starting from Toronto. What order of cities results in the shortest total path? This is variation on the classic travelling salesman problem (TSP) that has intrigued and bedevilled computational mathematicians for years. It is the rare mathematical challenge that is understandable by everyone and yet efforts to solve it have involved computer science, complexity theory, optimization theory and linear programming and influenced fields as diverse as logistics, genetics, manufacturing, telecommunications, astronomy, and neuroscience. [Read More]

The Beauty of Strange Attractors

Dynamic systems are those where something changes over time according to a set of rules. They are found in many fields of study including, physics, chemistry, geology, biology and economics. Examples include, the planets orbiting around the sun, the vibration of an airplane wing, and the diffusion of drugs in your body. In mathematics, the something that changes over time can be points in a plane that change according to the rules of a function, which in a general form looks like this: [Read More]

Who's a Buffon?

Estimating Pi

I wanted to try a simple interactive visualization using RStudio’s Shiny package and thought Buffon’s needle problem would work well. Around 1732, Georges-Louis Leclerc, Comte de Buffon, a French mathematician, first posed and solved the question that essentially boils down to asking what is the probability that a needle dropped on a floor of parallel lines crosses a line? He discovered that if the length of the needle is less than or equal to the width of the lines the probability is: [Read More]