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Voronoi Cones

Tom Walsh
A Voronoi diagram is a partitioning of a plane into regions such that each region contains one generating point and every point in a given region is closer to its generating point than to any other. GeoGebra has a built-in Voronoi function, where you input a list of points and GeoGebra will generate the Voronoi boundaries. After reading recently about how Voronoi diagrams can be generated through the use of cones, I decided to make this worksheet to demonstrate the idea. Each point represents the vertex of a cone. Move the points around and watch the pattern morph. The cones, when viewed directly from above, show the Voronoi pattern. Use the checkbox to show the Voronoi boundaries generated by the GeoGebra Voronoi function. Slide the slider to see the cones collapse or grow.