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
Inner regular measure from within by compact sets." Some authors use the term tight as a synonym for inner regular. This use of the term is closely related to tightness of a family of measures, since a finite measure "μ" is inner regular if and only if, for all "ε" > 0, there is some compact subset "K" of "X" such that "μ"("X" \ "K") < "ε". This is precisely the condition that the singleton collection of measures {"μ"} is tight. When the real line R is given its usual Euclidean topology, However, if the topology on R is changed, then these measures