Suppose the particle scatters off the target with polar angle and azimuthal angle plane.

This integral is evaluated setting , the elliptical Kepler orbit in polar angles.

It has the same basic properties as Graham's scan but eschews costly comparisons between polar angles.

The logarithmic spiral can be defined a curve whose polar tangential angle is constant.

However, pseudorapidity depends only on the polar angle of its trajectory, and not on the energy of the particle.

It is conjugate to the timelike polar angle which is also dimensionless.

Let θ be the conventional polar angle describing a planetary orbit.

It is customary to use θ, but this does not have to be the polar angle used in polar coordinate systems.

(A unit vector is determined by two spherical polar angles.)

Then it is easily seen that these edges of the convex polygon are ordered by polar angle.