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
Angle trisection equation with real coefficients can be solved geometrically with compass, straightedge, and an angle trisector if and only if it has three real roots. A regular polygon with "n" sides can be constructed with ruler, compass, and angle trisector if and only if formula_63 where "r, s, k" ≥ 0 and where the "p" are distinct primes greater than 3 of the form formula_64 (i.e. Pierpont primes greater than 3). For any nonzero integer , an angle of measure radians can be divided into equal parts with straightedge and compass if and only if is either a power of or