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4.2. The three-dimensional Fibonacci spiral
It is well known that the trigonometric sine and cosine can be defined as projection of the translational movement of a point on
the surface of an infinite rotating cylinder with the radius 1, whose symmetry center coincides with x-axis. Such a threedimensional
spiral is projected into the sine function on a plane and described by the complex function
f(x) = cos(x) + isin(x), where .
If we assume that the quasi-sine Fibonacci function (32) is a projection of a three-dimensional spiral on some funnel-shaped
surface, then analogous to the trigonometric sine, it is possible to construct a three-dimensional Fibonacci spiral.“ 137
Die eher unübliche dreidimensionale Darstellung der Spirale 138 zeigt anschaulich, warum die dreidimensionale
Darstellung gewählt wurde:
„Definition 2. The following function is a complex representation of the three-dimensional Fibonacci spiral:
51
. (34)
This function, by its shape, resembles a spiral that is drawn on the crater with a bent end (Fig. 4).
137 Stakhov/Rozin, The Golden Section, Fibonacci series and new hyperbolic models of Nature < URL >.
138 Stakhov/Rozin, The Golden Section, Fibonacci series and new hyperbolic models of Nature < URL >.