Spirals Based on the Fibonacci Sequence
A polar coordinate system can be used to create spirals based on the Fibonacci sequence with Mathematica. The formulas used to determine the nth Fibonacci number yield complex results when n is a non-integer. The internal algorithm employed by the Mathematica command
Another method of generating spirals from the Fibonacci sequence is based on the arrangement of adjacent squares that increase
in size following the sequence of Fibonacci numbers. This method always yields logarithmic spirals. A line drawn from the
origin to any point on such a spiral will form a constant angle with the tangent line at that point. It is unknown whether
the spirals r =
By manipulating the equations for the spirals in a three-dimensional parametric coordinate system, it is possible to produce graphic images that resemble shells.
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