Archimedean spiral [SEP] named after
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 of points 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
with real numbers "a" and "b". Changing the parameter "
measured orthogonally to both curves. There is a curve slightly different from the Archimedean spiral, the involute of a circle, whose turns have constant separation distance in the latter sense of parallel curves.
General Archimedean spiral.
Sometimes the term "Archimedean spiral" is used for the more general group of spirals
The normal Archimedean spiral occurs when "c" = 1. Other spirals falling into this group include the hyperbolic spiral ("c" = −1), Fermat's spiral ("c