This slide illustrates the eight-fold symmetry of a circle. To draw a complete circle we only need to calculate one eighth of the circle (known as an octant), and then reflect these points several times to obtain the whole circle.

We assume the center of the circle to be at the origin of the coordinate system. The initial octant is shown in yellow, on the top right of the circle. Now, we can reflect these points about the line x = y, to get the next octant clockwise, drawn in green. We now have a quadrant of the circle, and we can reflect all these points about the x-axis (the line y=0), to give the next quadrant (drawn cyan). Now we have a half circle, and if we reflect this about the y-axis (the line x = 0), we obtain the whole circle.