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 meridian as references. In astronomy, a given point on the celestial sphere (that is, the apparent position of an astronomical object) can be identified using any of several "astronomical coordinate systems", where the references vary according to the particular system. Astronomers measure the "angular separation" of two stars by imagining two lines through the centre of the Earth, each intersecting one of the stars. The angle between those lines can be measured, and is the angular separation between the two stars. In both geography and astronomy, a sighting direction can be specified in terms of a vertical angle such as