any point (, ) to the center: Mathematical "graph paper" is formed by imagining a 1×1 square centered around each cell (, ), where and are integers between − and . Squares whose center resides inside or exactly on the border of the circle can then be counted by testing whether, for each cell (, ), The total number of cells satisfying that condition thus approximates the area of the circle, which then can be used to calculate an approximation of . Closer approximations can be produced by using larger values of . Mathematically, this formula can be written: In other words, begin by choosing a value for . Consider all cells (, ) in which both and are integers between − and . Starting at 0, add 1 for each cell whose distance to the origin (0,0) is less than or equal to . When finished, divide the sum, representing the area of a circle of radius , by 2 to find the approximation of . For example, if is 5, then the cells considered are: {| style="font-size:75%;text-align:center;color:blue;height:1em" cellspacing="15" |- style="color:black" | (−5,5) || (−4,5) || (−3,5) || (−2,5) || (−1,5) || style="color:#bc1e47" | (0,5) || (1,5) || (2,5) || (3,5) || (4,5) || (5,5) |- | style="color:black" | (−5,4) || style="color:black" | (−4,4) || style="color:#bc1e47" | (−3,4) || (−2,4) || (−1,4) || (0,4) || (1,4) || (2,4) || style="color:#bc1e47" | (3,4) || style="color:black" | (4,4) || style="color:black" | (5,4) |- | style="color:black" | (−5,3) || style="color:#bc1e47" | (−4,3) || (−3,3) || (−2,3) || (−1,3) || (0,3) || (1,3) || (2,3) || (3,3) || style="color:#bc1e47" | (4,3) || style="color:black" | (5,3) |- | style="color:black" | (−5,2) || (−4,2) || (−3,2) || (−2,2) || (−1,2) || (0,2) || (1,2) || (2,2) || (3,2) || (4,2) || style="color:black" | (5,2) |- | style="color:black" | (−5,1) || (−4,1) || (−3,1) || (−2,1) || (−1,1) || (0,1) || (1,1) || (2,1) || (3,1) || (4,1) || style="color:black" | (5,1) |- | style="color:#bc1e47" | (−5,0) || (−4,0) || (−3,0) || (−2,0) || (−1,0) || (0,0) || (1,0) || (2,0) || (3,0) || (4,0) || style="color:#bc1e47" | (5,0) |- | style="color:black" | (−5,−1) || (−4,−1) || (−3,−1) || (−2,−1) || (−1,−1) || (0,−1) || (1,−1) || (2,−1) || (3,−1) || (4,−1) || style="color:black" | (5,−1) |- | style="color:black" | (−5,−2) || (−4,−2) || (−3,−2) || (−2,−2) || (−1,−2) || (0,−2) || (1,−2) || (2,−2) ||