Pitch angle of a spiral

Equivalently, it is the complementary angle to the angle made by the vector from the origin to a point on the spiral, with the tangent vector of the spiral at the same point.

[1] Pitch angles are frequently used in astronomy to characterize the shape of spiral galaxies.

[3] Logarithmic spirals are characterized by the property that the pitch angle remains invariant for all points of the spiral.

For instance, only the golden spiral has pitch angle

For an Archimedean spiral the angle decreases with the distance, while for a hyperbolic spiral the angle increases with the distance.