Position angle a hypothetical binary star with a PA of 135 degrees, that means an imaginary line in the eyepiece drawn from the north celestial pole to the primary (P) would be offset from the secondary (S) such that the NCP-P-S angle would be 135 degrees. When graphing visual binary orbits, the NCP line is traditionally drawn downward—that is, with north at bottom—and PA is measured counterclockwise. Also the direction of the proper motion can for example be given by its position angle. The definition of position angle is also applied to extended objects like galaxies, where it refers to the angle
Octagon is then as above: Expressed in terms of the span, the area is Another simple formula for the area is More often the span "S" is known, and the length of the sides, "a", is to be determined, as when cutting a square piece of material into a regular octagon. From the above, The two end lengths "e" on each side (the leg lengths of the triangles (green in the image) truncated from the square), as well as being formula_12 may be calculated as The circumradius of the regular octagon in terms of the side length "a" is and the