Pitch angle of a spiral

In the geometry of

Logarithmic spirals are characterized by the property that the pitch angle remains invariant for all points of the spiral. Two logarithmic spirals are congruent when they have the same pitch angle, but otherwise are not congruent. For instance, only the golden spiral has pitch angle

$${\displaystyle \arctan \left({\frac {\ln \varphi }{\pi /2}}\right)\approx 17^{\circ },}$$

${\displaystyle \varphi }$

Spirals that are not logarithmic have pitch angles that vary by distance from the center of the spiral. For an Archimedean spiral the angle decreases with the distance, while for a hyperbolic spiral the angle increases with the distance.^[3]

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