Imagine a city with several hospitals. When someone has an emergency, you’d like them to always go, or be taken, to the hospital that’s nearest to where they currently are. What you need is a map showing each hospital’s catchment area: for anyone in that region, that hospital is closer than any other. How do you do that? You create edges around the hospitals using a step-by-step approach until you have accounted for all the hospitals. The picture you get at the end, the division of the map into regions of points that are all closer to one of the given points than any other, is called a Voronoi diagram. It’s named after the Russian mathematician Gregory Voronoi (1868-1908).
We utilised math through an in-class activity which we partook in was based on real life application of Voronoi diagrams. Here we used chalk, meter rulers and coloured tapes on the grids of the classroom floor as our basis for a graph, forming an x and y axis and developing from there. We created our four coordinates which were sites A, B, C & D. From here we calculated mid points, perpendicular bisectors, slopes and then created edges around them. This allows us to further understand the use of maps in the current times and how to determine our proximity to a closest site. We used collaboration as a class, calculating math, drawing the edges, and eventually forming the diagram. Gaining a high ground, we used the chairs to overlook the graph and interpret it further. Overall, our class learnt through collaboration, communication, and inquiry the step-by-step process of creating a Voronoi diagram. This hands-on activity allowed us to learn actively through kinaesthetic movements, which transparently reflected our choices in mathematical processes.
Written by DP-2 AI Students
PlusMath. n.d. 19 October 2022. <https://plus.maths.org/content/maths-minute-voronoi-diagrams>.