Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Lattice points on a circle.

  1. Nov 4, 2012 #1
    Does any circle having irrational radius have no lattice points on its boundary ?
    Extended question: Is there any way to determine the number of lattice points lying on the boundary of a given circle ?
    *The centres of these circles are all (0,0) *
     
    Last edited: Nov 4, 2012
  2. jcsd
  3. Nov 4, 2012 #2
    What do you mean by lattice points? Points (x,y) where x and y are integers?

    The circle with radius 1/sqrt(2) comes to my mind.
     
  4. Nov 4, 2012 #3
    Thanks, but the equation x^2 + y^2 =1/2 seems to have no integer solution...
     
  5. Nov 4, 2012 #4

    pwsnafu

    User Avatar
    Science Advisor

    Isn't that what you asked for?
     
  6. Nov 4, 2012 #5
    Ah, my bad :tongue:, I meant to ask if EVERY circle having irrational radius have no lattice points on its boundary, not an example :smile:.
     
  7. Nov 4, 2012 #6
    The boundaries of many circles having an irrational radius contain lattices points. For example, can you find lattice points on a circle of radius √2? What about one with radius √5?
     
  8. Nov 4, 2012 #7
    Thanks, I didn't think thoroughly before posting this silly question, sorry.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Lattice points on a circle.
  1. Lattice Points (Replies: 7)

Loading...