Problem 210

Obtuse Angled Triangles

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° So, for example, N(4)=24 and N(8)=100.

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° So, for example, N(4)=24 and N(8)=100.

What is N(1,000,000,000)?

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These problems are part of
Project Euler
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CC BY-NC-SA 2.0 UK
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