The Centerpoint Theorem states that for any set of points in a d-dimensional space, there exists a point (the centerpoint) that lies within a certain distance from at least a fraction of the points in the set. This theorem emphasizes the existence of a point that can be deemed 'central' in the sense that it minimizes the maximum distance to any point in the set. It plays a crucial role in understanding geometric structures and their properties, especially when analyzing incidences between points and hyperplanes.
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