Octagon eight lines of reflective symmetry and rotational symmetry of order 8. A regular octagon is represented by the Schläfli symbol {8}. The internal angle at each vertex of a regular octagon is 135° (formula_1 radians). The central angle is 45° (formula_2 radians). The area of a regular octagon of side length "a" is given by In terms of the circumradius "R", the area is In terms of the apothem "r" (see also inscribed figure), the area is These last two coefficients bracket the value of pi, the area of the unit circle. The area can also be expressed as where
Angle or "terminal side" is defined by the measure from the initial side in radians, degrees, or turns. With "positive angles" representing rotations toward the positive y-axis and "negative angles" representing rotations toward the negative "y"-axis. When Cartesian coordinates are represented by "standard position", defined by the "x"-axis rightward and the "y"-axis upward, positive rotations are anticlockwise and negative rotations are clockwise. In many contexts, an angle of −"θ" is effectively equivalent to an angle of "one full turn minus "θ"". For example, an orientation represented as −45° is effectively equivalent to an orientation represented as 360° − 45° or 315°.