MathDB
Rectangle Pixelations

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August 8, 2024
rectangleexpected value2022

Problem Statement

Let RR be the rectangle in the coordinate plane with corners (0,0)(0, 0), (20,0)(20, 0), (20,22)(20, 22), and (0,22)(0, 22), and partition RR into a 20×2220\times 22 grid of unit squares. For a given line in the coordinate plane, let its pixelation be the set of grid squares in RR that contain part of the line in their interior. If PP is a point chosen uniformly at random in RR, then compute the expected number of sets of grid squares that are pixelations of some line through PP.
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