A squircle [skwer-kul] is a mathematical shape with properties between those of a square and those of a circle. It is a special case of superellipse. The word ‘squircle’ is a portmanteau of the words ‘square’ and ‘circle.’ A shape similar to a squircle, called a rounded square, may be generated by arranging four quarters of a circle and connecting their loose ends with straight lines. Although constructing a rounded square may be conceptually and physically simpler, the squircle has the simpler equation and can be generalized much more easily. One consequence of this is that the squircle and other superellipses can be scaled up or down quite easily. This is useful where, for example, one wishes to create nested squircles.
Squircles are useful in optics. If light is passed through a two-dimensional square aperture, the central spot in the diffraction pattern can be closely modeled by a squircle (also called a supercircle). If a rectangular aperture is used, the spot can be approximated by a superellipse. Squircles have also been used to construct dinner plates. A squircular plate has a larger area (and can thus hold more food) than a circular one with the same radius, but still occupies the same amount of space in a rectangular or square cupboard. The same is true of a square plate, but there are various problems (such as wiping up sauce) associated with the corners of square plates.
The Daily Omnivore 