RSS FeedUse secure connection  Obtuse Angled Triangles  Problem
210  Published on Friday, 26th September 2008, 10:00 pm; Solved
by 1051 Consider the set S(r) of points (x,y) with integer
coordinates satisfying |x| + |y| ≤ r. Let O be the point (0,0)
and C the point (r/4,r/4). Let N(r) be the number of points B in
S(r), so that the triangle OBC has an obtuse angle, i.e. the
largest angle α satisfies 90°<α<180°. So, for example, N(4)=24
and N(8)=100.  What is N(1,000,000,000)?