How Does the Ratio of Lattice Points to Radius Behave as Radius Increases?

Join the discussion
Registration is free. Start your own thread to ask a follow-up.
Sign up Log in
1 reply · 3K views
Shoelace Thm.
Messages
59
Reaction score
0
Given a circle centered at the origin, how can one prove that the limit of the quotient of the number of lattice points on the circle over the radius goes to zero as radius goes to infinity?
 
Physics news on Phys.org

Discussion

Similar threads

How Much Should the Radius Increase to Enlarge the Circle's Area by b Units?
  • mathdad
  • · Replies 4 ·
  • Calculus
Replies
4
How Does a 3% Increase in Radius Affect Blood Flow?
  • tc903
  • · Replies 1 ·
  • Calculus
Replies
1
Graduate Lattice Points on Circle: Determining the Number of Points on the Boundary
  • funcalys
  • · Replies 6 ·
  • Linear and Abstract Algebra
Replies
6
Undergrad Counting Lattice Points in a Circle: A Math Contest Question
  • yik-boh
  • · Replies 7 ·
  • Linear and Abstract Algebra
Replies
7
Why Does a Smaller Radius Increase Centripetal Force?
  • cclixn
  • · Replies 1 ·
  • Introductory Physics Homework Help
Replies
1
Change in GPE of the moon as the radius increases. Getting extreme answers
  • psychicgerm
  • · Replies 6 ·
  • Introductory Physics Homework Help
Replies
6
Undergrad Why doesn't expanding light from a star get dimmer as its radius increases?
  • vorcil
  • · Replies 16 ·
  • Astronomy, Astrophysics, Cosmology
Replies
16
Graduate How does a Penning trap determine the upper limit of the electron radius?
  • granpa
  • · Replies 4 ·
  • High Energy, Nuclear, Particle Physics
Replies
4