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
Radon measure regular, and locally finite, and inner regular for open sets. It coincides with "m" on compact and open sets, and "m" can be reconstructed from "M" as the unique inner regular measure that is the same as "M" on compact sets. The measure "m" is called moderated if "M" is σ-finite; in this case the measures "m" and "M" are the same. (If "m" is σ-finite this does not imply that "M" is σ-finite, so being moderated is stronger than being σ-finite.) On a strongly Lindelöf space every Radon measure is moderated. An example of a measure "m" that is