A circle of radius 5 with its center at (0,0) is drawn on a Cartesian coordiante system. How many lattice points lie within or on this circle?
+128406 We will have 4(5) + 1 = 21 lattice points on the x, y axis
To find the number of the rest of the points we have
4 [ floor (sqrt [ 5^2 - 1^2]) + floor (sqrt [ 5^2 - 2^2 ]) + floor (sqrt [ 5^2 - 3^2 ]) + floor( sqrt [ 5^2 - 4^2] ) ] =
4 [ floor [sqrt (24) ] + floor [ sqrt ( 21) ] + floor [sqrt ( 16 ) ] + floor [sqrt (9) ] ] =
4 [ 4 + 4 + 4 + 3 ] =
4 [ 15 ] =
60
So...the total number of lattice points = 21 + 60 = 81
