Editing Polar coordinate system (section)

===Archimedean spiral===
[[File:Spiral of Archimedes.svg|thumb|right|One arm of an Archimedean spiral with equation {{math|1=''r''(''φ'') = ''φ'' / 2''π''}} for {{math|0 < ''φ'' < 6''π''}}]]
The [[Archimedean spiral]] is a spiral discovered by [[Archimedes]] which can also be expressed as a simple polar equation. It is represented by the equation
<math display="block">r(\varphi) = a + b\varphi. </math>
Changing the parameter ''a'' will turn the spiral, while ''b'' controls the distance between the arms, which for a given spiral is always constant. The Archimedean spiral has two arms, one for {{math|''φ'' > 0}} and one for {{math|''φ'' < 0}}. The two arms are smoothly connected at the pole. If {{math|1=''a'' = 0}}, taking the mirror image of one arm across the 90°/270° line will yield the other arm. This curve is notable as one of the first curves, after the [[conic section]]s, to be described in a mathematical treatise, and as a prime example of a curve best defined by a polar equation.
{{Clear}}[[Image:Elps-slr.svg|thumb|Ellipse, showing semi-latus rectum]]