current community
chat
blog
MathOverflow
MathOverflow Meta
your communities
Sign up
or
log in
to customize your list.
more stack exchange communities
Stack Exchange
sign up
log in
tour
help
Tour
Start here for a quick overview of the site
Help Center
Detailed answers to any questions you might have
Meta
Discuss the workings and policies of this site
MathOverflow
Questions
Tags
Users
Badges
Unanswered
Ask Question
user27203
less info
network profile
62
reputation
5
bio
website
location
age
visits
member for
2 years
seen
Nov 1 '12 at 8:58
stats
profile views
123
62
reputation
bio
website
visits
member for
2 years
5
badges
location
seen
Nov 1 '12 at 8:58
summary
answers
questions
tags
badges
favorites
bounties
reputation
activity
40
Actions
suggestions
reviews
revisions
comments
badges
posts
accepts
all
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...
MathOverflow works best with JavaScript enabled