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user27203
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Oct
25
revised
Properties of the minimum circumscribing circle for points sequentially placed within a circle of radius $r$ of previously placed points on a 2D plane
added 36 characters in body
Oct
25
asked
Properties of the minimum circumscribing circle for points sequentially placed within a circle of radius $r$ of previously placed points on a 2D plane
Oct
21
awarded
Supporter
Oct
21
accepted
Maximizing the number of lattice points in a circle of radius $r$ placed on a lattice
Oct
21
comment
Maximizing the number of lattice points in a circle of radius $r$ placed on a lattice
Ahem, peaks in terms of the number of lattice points internal to the circle.
Oct
21
comment
Maximizing the number of lattice points in a circle of radius $r$ placed on a lattice
@Michael Biro If a circle of radius $r$ were to execute something like a Brownian motion on a lattice, would we really only expect peaks when its center drifts over a small set of points in the fundamental unit of the Z^2 or A^2 lattices?
Oct
21
comment
Maximizing the number of lattice points in a circle of radius $r$ placed on a lattice
@Michael Biro "I want to say that by symmetry, the only relevant centers are lattice points, midpoints of square edges, and centers of squares..." right, I think that makes a lot of sense... but is there any way to make this statement rigorous?
Oct
21
revised
Maximizing the number of lattice points in a circle of radius $r$ placed on a lattice
deleted 20 characters in body
Oct
21
revised
Maximizing the number of lattice points in a circle of radius $r$ placed on a lattice
added 322 characters in body; deleted 5 characters in body; added 121 characters in body
Oct
21
revised
Maximizing the number of lattice points in a circle of radius $r$ placed on a lattice
added 558 characters in body; added 1 characters in body
Oct
21
revised
Maximizing the number of lattice points in a circle of radius $r$ placed on a lattice
added 499 characters in body
Oct
21
revised
Maximizing the number of lattice points in a circle of radius $r$ placed on a lattice
added 93 characters in body
Oct
21
revised
Maximizing the number of lattice points in a circle of radius $r$ placed on a lattice
added 10 characters in body; deleted 10 characters in body
Oct
21
asked
Maximizing the number of lattice points in a circle of radius $r$ placed on a lattice
Oct
20
accepted
An exact counting solution for the number of points within a circle of radius $r$ centered on a lattice point in a $A_2$ hexagonal lattice
Oct
20
comment
An exact counting solution for the number of points within a circle of radius $r$ centered on a lattice point in a $A_2$ hexagonal lattice
@Yoav I was following what Will Sawin was doing, but to make sure I understand, could you quickly note your approach?
Oct
20
awarded
Commentator
Oct
20
comment
An exact counting solution for the number of points within a circle of radius $r$ centered on a lattice point in a $A_2$ hexagonal lattice
@Will Sawin Hmm... I don't see the error.
Oct
20
revised
An exact counting solution for the number of points within a circle of radius $r$ centered on a lattice point in a $A_2$ hexagonal lattice
added 316 characters in body; added 1 characters in body
Oct
20
comment
An exact counting solution for the number of points within a circle of radius $r$ centered on a lattice point in a $A_2$ hexagonal lattice
With: Table[1 + 2*Floor[r] + 2*Floor[r/3^(1/2)] + 4*Sum[Floor[((4*r^2 - 4*i^2)/3)^(1/2)], {i, 1, Floor[r]}] + 4*Sum[Floor[((4*r^2 - (2*i + 1)^2)/3)^(1/2) + 1/2], {i, 0, Floor[r - 1/2]}], {r, 0, 10}] ... I'm getting the table: {1, 7, 31, 61, 117, 179, 259, 351, 457, 573, 723}, which doesn't match anything in OEIS...
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