The Spiral of Archimedes
The spiral plotted above is one branch of a curve known as the spiral of Archimedes. In fact, it is part of a family of spirals, many of which have different names. Some examples are given below.
where a is the radius of the spiral, and n is some real number. In the case n = 1, plotted at the top of the page, the spiral is called the spiral of Archimedes. The family of spirals also has the polar parameterization
Several values of n other than 1 are also given specific names: