If *n* is equal to 2, then it describes an ellipse (if *a* = *b*, then it describes a circle).

If n is greater than 2, then this is a "superellipse" (if *a* = *b*, then this is a supercircle).

As *n* increases, the ellipse becomes more "rectangularish", and as *n* approaches ∞, the limit *is* a rectangle (or a square if a=b).

What value must *n* have such that the figure has an area exactly halfway between the associated ellipse (when n=2) and rectangle (when n=∞)?

The graphs below, calculated by varying *n* with *a* = *b* = 1, show this property. Note that as *n* approaches zero, the curve degenerates into two crossed lines along the x- and y-axes.