Editing Polar coordinate system (section)

===Modeling===
Systems displaying [[radial symmetry]] provide natural settings for the polar coordinate system, with the central point acting as the pole. A prime example of this usage is the [[groundwater flow equation]] when applied to radially symmetric wells. Systems with a [[central force|radial force]] are also good candidates for the use of the polar coordinate system. These systems include [[gravitation|gravitational fields]], which obey the [[inverse-square law]], as well as systems with [[point source]]s, such as [[antenna (radio)|radio antennas]].

Radially asymmetric systems may also be modeled with polar coordinates. For example, a [[microphone]]'s [[Microphone pick up patterns|pickup pattern]] illustrates its proportional response to an incoming sound from a given direction, and these patterns can be represented as polar curves. The curve for a standard cardioid microphone, the most common unidirectional microphone, can be represented as {{nowrap|''r'' {{=}} 0.5 + 0.5sin(''ϕ'')}} at its target design frequency.<ref>{{Cite book |last=Eargle |first=John |title=Handbook of Recording Engineering |publisher=Springer |year=2005 |isbn=0-387-28470-2 |edition=Fourth |author-link=John M. Eargle}}</ref> The pattern shifts toward omnidirectionality at lower frequencies.