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 Inner regular measure In mathematics, an inner regular measure is one for which the measure of a set can be approximated from within by compact subsets. Let ("X", "T") be a Hausdorff topological space and let Σ be a σ-algebra on "X" that contains the topology "T" (so that every open set is a measurable set, and Σ is at least as fine as the Borel σ-algebra on "X"). Then a measure "μ" on the measurable space ("X", Σ) is called inner regular if, for every set "A" in Σ, This property is sometimes referred to in words as "approximation