Archimedean spiral

The Archimedean spiral (also known as the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes. It is the locus corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line that rotates with constant angular velocity. Equivalently, in polar coordinates $(r, θ)$ it can be described by the equation

r=b\cdot \theta

with real number $b$ . Changing the parameter $b$ controls the distance between loops.

From the above equation, it can thus be stated: position of particle from point of start is proportional to angle $θ$ as time elapses.

Archimedes described such a spiral in his book On Spirals. Conon of Samos was a friend of his and Pappus states that this spiral was discovered by Conon.

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