The ellipse is well known to students of mathematics at an advanced high school level and at an undergraduate level through its associations with, say, conic sections and their deployment as hardware in dual reflector antenna systems. Perhaps less well known is its appearance on the software side, so to speak, for example in RF (Radio Frequency) engineering in the context of polarisation, where it is known as the polarisation ellipse. It is the purpose here to discuss this manifestation and dwell particularly on the concept of a circumscribing rectangle for this ellipse because such aspects are of interest to the RF engineer who may be involved with measurements to determine its properties. This exercise affords an interesting insight into a very practical application of tertiary level mathematics and whilst it is of course helpful to appreciate the physical concepts involved, a lack of such knowledge does not detract from an appreciation of the underlying sums, which should be within the grasp of the above, interested student.