Spiral equiangular

In Fig. 10.3 it is seen that, if both Vr and Vu vary inversely to the radius r, the angle a is constant. Hence for such a case the path line is the equiangular or logarithmic spiral. For a case where B varies, Vr will not vary in the same way as Vu, and hence the angle a is not a constant. 

Through a set of initial points on adjoining five-fold axes a set of 20 intersecting equiangular spirals can be drawn emanating from any chosen origin. 

Possible arrangements for spatial nets , a rectangular net b equiangular spiral c... 

Ali, S. and A. H. Zaidi, Head Loss and Critical Reynolds Numbers for Flow in Ascending Equiangular Spiral Tube Coils, Ind. Eng. Chem. Proc. Des. Dev. 18, 349-353 (1979). 

Fig. 3 A golden spind inscribed in a golden rectangle defined by a Fibonacci sequence. The increasing size of successive squares is defined by the Fibonacci labels ( ), and the ratio of their side lengths approaches r as —> oo. The inscribed spiral approximates an equiangular logeirithmic spiral [4]...

It has been argued [8] that the transformation from curved space-time to Euclidean tangent space is described by the golden ratio. This is not an entirely unexpected conclusion, in view of the prominence of r in the operation of selfsimilar symmetries, related to equiangular logarithmic spirals. 

Combination of these two operations represents a continuous dilative rotation that transforms the general point (r, 9) into (a r, 6 +1), as t changes continuously. The locus of the transform of (a, 0) is the equiangular spiral... 

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