This problem is looking for the number of vertices on the hexagonal grid inside the circle of radius r. The center of the hexagon is not counted as a point for this problem, and this is true for every hexagon inside the circle.
surface of a spherical planet
Set some matrix elements to zero
frame of the matrix
Side of a rhombus
Shifted Hexagonal Tiling Dots in a Circle
Dots in a Diamond
Edges of a n-dimensional Hypercube
Dots in a Sphere
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