Avoiding Colinear Points

[Leroy Quet]

Richard Guy wrote:

>I got the no-three-in-line problem from
>Heilbronn over 50 years ago.  See F4 in
>UPINT.  In Canad. Math. Bull. 11 (1968)
>527--531; MR 39 #129 Guy & Kelly conjecture
>that, for large n, at most  (c + eps)n
>points can be selected, where  3c^3 = 2pi^2
>i.e. c ~ 1.85.  Curiously, as recently as
>last March, Gabor Ellmann pointed out an
>error in our heuristic reasoning, which,
>when corrected, gives  3c^2 = pi^2, or
>c ~ 1.813799.  I should send a correction
>to Canad Math Bull!     R.

And you better send a correction to Mathworld too.
:)

http://mathworld.wolfram.com/IntegerLattice.html


Leroy Quet