# Logarithmic spiral

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 a spiral curve such that radii drawn from its pole or eye at equal angles with each other are in continual proportion. See Spiral.

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Handzic started with Archimedean spirals and logarithmic spirals.
In a logarithmic spiral, this angle, the spiral's "camming angle," never varies.
The device used four spring-loaded cams, each shaped like a logarithmic spiral.
Phyllotaxis also shows that not only do leaves grow around a stem using this angle, and not only do the florets on the head of a sunflower grow accordingly, but they also grow in interleaving logarithmic spirals which number according to Fibonacci pairs.
22) The logarithmic spiral is thus closely connected to the Golden Ratio.
There has been a lot of material written about logarithmic spirals of golden proportion but I have never come across an article which states the exact equation of the spiral which ultimately spirals tangentially to the sides of the rectangles as in Figure 1.
In articles associated with such diagrams, it is often stated, that the curve thus obtained approximates a logarithmic spiral of golden proportion.
I started out with logarithmic spirals that vary in intervals as they move outward.
Thus, the processes that lead to the formation of logarithmic spirals in seashells and animal horns seem to operate through the intricate relationships between the Fibonacci sequence and the golden section.
181), one can construct a logarithmic spiral (a spiral in which the logarithm of the radial distance from the center increases in proportion to the total angle traversed along the spiral).
The logarithmic spiral is also known as the growth spiral or the equiangular spiral.
The logarithmic spiral can be defined as a curve that exhibits a constant angle between the radius vector (a line from the centre to a point on the curve) and the tangent vector (a line oriented along the path of travel).

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