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
Borel regular measure becomes a full measure (countably additive) if restricted to the Borel sets. Borel regular measure In mathematics, an outer measure "μ" on "n"-dimensional Euclidean space R is called a Borel regular measure if the following two conditions hold: An outer measure satisfying only the first of these two requirements is called a "Borel measure", while an outer measure satisfying only the second requirement (with the Borel set B replaced by a measurable set B) is called a "regular measure". The Lebesgue outer measure on R is an example of a Borel regular measure. It can be proved that a Borel