Archimedean spiral

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

with real numbers a and b. Changing the parameter a will turn the spiral, while b controls the distance between successive turnings.

Archimedes described such a spiral in his book On Spirals.

Characteristics

The Archimedean spiral has the property that any ray from the origin intersects successive turnings of the spiral in points with a constant separation distance (equal to 2πb if θ is measured in radians), hence the name "arithmetic spiral".

In contrast to this, in a logarithmic spiral these distances, as well as the distances of the intersection points measured from the origin, form a geometric progression.