+24 A circle of radius 5 with its center at the origin is drawn on a Cartesian coordinate system. How many lattice points (points with integer coordinates) lie within or on this circle?
+658 Hint: Use the pythagorean theorem. In other words, how many pythagorean triples can you find?
+129899 Number of latttice points =
5 * 4 + 1 = 21 points on the axis
Plus
4 * [ greatest integer [ sqrt ( 25 - 1^2)] + greatest integer [ sqrt (25 - 2^2) ] + greatest integer [ sqrt (25 - 3^2) ] + greatest integer [ sqrt (25 - 4^2 ] ] =
4 [ 4 + 4 + 4 + 3 ] = 4 [ 15] = 60
So....total lattice points = 21 + 60 = 81
