In 1992, Manuel Fernandez-Guasti introduced a smooth algebraic curve that lies between the circle and the square.

The curve has two parameters:

*radius*and

**r***squareness*

**s**This is a quartic curve (i.e. degree 4) because of the x²y² term.

When s = 0, the FG-squircle is a circle with radius r.

When s = 1, the FG-squircle is a square with side length 2r.

In between, it is a shape that resembles both the circle and the square

Note: For this discussion, we are mainly interested with the curve located in the region

-r ≤ x ≤ r and -r ≤ y ≤ r

This quartic polynomial equation can have values for (x,y) outside this scope, but we can ignore those 4 extraneous regions.

for Fernandez-Guasti's original paper.

See also my paper https://arxiv.org/ftp/arxiv/papers/1604/1604.02174.pdf

for more details.

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