Number (0): Everything in this space must add up to 0. The answer is 4-0, placed horizontally; 0-0, placed horizontally; 0-2, placed vertically.
When another data point is inserted and the Voronoi diagram reconstructed, the newly created region displaces the area that once belonged to the old regions. Those points whose regions were displaced are considered natural neighbours to the new point. The weight of each natural neighbour is given by the area taken from the total area occupied by the new region. In 3D, we measure polyhedral volumes instead of areas.
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This was not the first time that microbiologists experienced problems with agar. A phenomenon called “The Great Plate Count Anomaly” baffled researchers in the early 20th century when they observed that the number of cells seen under a microscope didn’t match the actual number of colonies growing on an agar plate. Investigating this discrepancy, researchers found agar itself to be the culprit: when nutrient broths are heated with agar during boiling, harmful byproducts (hydroperoxide) can form due to the reaction of agar with phosphate minerals contained in the media. Researchers can avoid this by autoclaving agar separately from the nutrient broth, or by reducing the amount of agar used.