IU mathematician credited with solving one of combinatorial geometry's most challenging problems: IU News Room: Indiana University: "If someone hands you some distinct set of points, you can figure out what is the set of differences. The problem is to determine what the minimum possible set of distances is," Katz said. "What we did is to show that no matter how you place the N points, the number of distances is at least a constant times N/log N..."
Combinatorial geometry, a field that has far-reaching applications in areas as diverse as drug development, robot motion planning and computer graphics, examines discrete properties like symmetry, folding, packing, decomposition and tiling associated with combinations of geometric objects.
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