[seqfan] No isosceles triangles in a square grid, continued

Neil Sloane njasloane at gmail.com
Sun Apr 24 22:30:21 CEST 2016


There is now an entry (A271914) for the array
T(m,n) = max number of points in mXn grid
such that no three form an isosceles triangle.

Initially I had conjectured that the answer was usually m+n-2,
(prompted by Giovanni's results for T(n,n))
but then Rob found many examples where it was m+n-1,
so then I thought it would always be either m+n-2 or m+n-1.
But then Rob pointed out that he had found T(6,9) =12 = m+n-3.

So now this is quite mysterious.

I still believe however that "If an mXn grid contains m+n points then
three of them form an isosceles triangle", since it sounds
so pretty. And I "almost" had a proof last night.

This is a new thread, there was too much baggage in the old one.


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