Logarithmic Spirals: Constant Pitch Angle

The pitch angle, , is defined as the angle between the arm and the tangent circle. Clearly: tan = dr / rd, where is the azimuthal angle.

Since tan is often roughly constant, then the equation for the arm is: tan d = dr / r

Integrating, we get: ( - _o)tan = ln r - ln r_o, or, equivalently: r() = r_o exp[ ( - _o) tan ]