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
Perceived visual angle "S′" describes the Ebbinghaus illusion and many other classic "size" illusions more completely and more logically than does the popular SDIH. What still needs to be explained, however, is why the basic visual angle illusion occurs in each example. Describing the few existing explanations for visual angle illusions is beyond the scope of this present entry. The most recent theories have been presented mostly in articles concerning the moon illusion (Baird et al., 1990, Enright, 1989a, 1989b, Hershenson, 1982, 1989b, Higashiyama, 1992, McCready 1986, 1999–2007, Plug & Ross, 1989, Reed, 1989, Roscoe, 1989, and especially in two "moon illusion" books