Squircular Calculations
  The Fernandez-Guasti squircle is a plane algebraic curve that is an intermediate shape between the circle and the square. In this paper, we will analyze this curve and derive formulas for its area and polar form. We will also provide several parametric equations of the squircle. Finally, we extend the squircle to three dimensions by coming up with an analogous surface that is an intermediate shape between the sphere and the cube. 
Chamberlain Fong
math.GM