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Text File  |  1992-12-30  |  1.0 KB  |  28 lines
  1. Newsgroups: sci.math.research
  2. Path: sparky!uunet!zaphod.mps.ohio-state.edu!sdd.hp.com!ux1.cso.uiuc.edu!news.cso.uiuc.edu!dan
  3. From: johnmpaz@phoenix.princeton.edu (John Manuel Paz)
  4. Subject: nearest points
  5. Nntp-Posting-Host: atbat.princeton.edu
  6. Message-ID: <1992Dec30.032510.25183@Princeton.EDU>
  7. Originator: dan@symcom.math.uiuc.edu
  8. Sender: Daniel Grayson <dan@math.uiuc.edu>
  9. X-Submissions-To: sci-math-research@uiuc.edu
  10. Organization: Princeton University
  11. X-Administrivia-To: sci-math-research-request@uiuc.edu
  12. Approved: Daniel Grayson <dan@math.uiuc.edu>
  13. Date: Wed, 30 Dec 1992 03:25:10 GMT
  14. Keywords: number theory
  15. Lines: 11
  16.  
  17. Hi,
  18.     In "Number Theory" Hardy presents a result which shows that the
  19. closest rational approximation to an irrational number is:
  20.  
  21.     | r - p/q | <= 1/q^2,    r - irrational, 0<p<=q, p, q rational
  22.  
  23. which is the same thing as saying the closest point of an approximating
  24. lattice to a line is O(1/q^2).  I was wondering if anyone could direct
  25. me to any results concerning circles or any curves with curvature.
  26. Thanks in advance.
  27.  
  28.