Editing Archimedean spiral (section)

==Characteristics==
[[File:Archimedean spiral polar.svg|right|thumb|upright=1.2|Archimedean spiral represented on a polar graph]]
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 {{math|2''[[Pi|π]]b''}} if {{mvar|θ}} is measured in [[radian]]s), 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]].

The Archimedean spiral has two arms, one for {{math|''θ'' > 0}} and one for {{math|''θ'' < 0}}. The two arms are smoothly connected at the origin. Only one arm is shown on the accompanying graph. Taking the mirror image of this arm across the {{mvar|y}}-axis will yield the other arm.

For large {{mvar|θ}} a point moves with well-approximated uniform acceleration along the Archimedean spiral while the spiral corresponds 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<ref>{{Cite OEIS|1=A091154}}</ref> (see contribution from Mikhail Gaichenkov).

As the Archimedean spiral grows, its [[evolute]] asymptotically approaches a circle with radius {{math|{{sfrac|{{abs|''v''}}|''ω''}}}}.