Area is only a linear function of distance when an edge is axis-aligned.
The area of your second square is 0.5, so if I’m not mistaken the fraction of the total area is 0.25, same as the first square.
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I’m using proportions. Count the triangles. Each quadrant has 4. Each is 1/16 of the total. Only 2 are covered, i.e. 1/8 of the total pixel area.
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But your pixel square doesn’t have side length 1, so it’s not comparable. I’m measuring exact distance from center of pixel square to edge.
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