An ellipse is ellipse-shaped, of course! Every mathematician knows what an ellipse looks like – at least, this is generally true in the Cartesian plane, with the standard distance function or metric. However, there are other metrics which can be applied to the plane ℝ2 and it might be useful to know what an ellipse looks like when distances are defined by these metrics. The set of points under consideration will be ℝ2, the real plane, and the metrics under consideration will be the standard metric, the Manhattan (or taxi-cab) metric and the maximum modulus metric.