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.
Snakes on a plane
Spherical radius given four points
Chebyshev polynomials of the 1st Kind
length of a vector
Dots in a Sphere
Generalized Laguerre polynomials
Triangular Tiling Dots in a Circle
Radial Zernike polynomials
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