It begins at an infinite distance from the pole in the centre, it winds faster and faster around as it approaches the pole, the distance from any point to the pole, following the curve, is infinite. The following is a parametric representation in Euclidean coordinates:
x = a/t cos t
y = a/t sin t
where t is a parameter. It has an asymptote at y = a.
This Archimedean spiral is distinguished from the logarithmic spiral by the fact that successive turnings of the spiral have a constant separation distance (equal to 2πb if θ is measured in radians), while in a logarithmic spiral these distances form a geometric progression.
Virtually all static spirals appearing in nature are logarithmic spirals, not Archimedean ones.
Many dynamic spirals (such as the Parker spiral of the solar wind, or the pattern made by a St.
Feeds |
Contact