Angle of Intersection for Equiangular Spirals
The polar equation for an equiangular spiral is . You can vary the values of , , and to see that the angle of intersection remains constant, independent of . This means that, given arbitrary constants and , the acute angle formed between any radial vector to a point on the curve and the tangent line to the curve at that point remains the same for all values of .
 R. M. Young, Excursions in Calculus: An Interplay of the Continuous and the Discrete, Washington, D.C.: Mathematical Association of America, 1992.