Definition: A superellipse, also known as a Lamé curve (named after Gabriel Lamé),
is a closed curve defined by the equation |x/a|n + |y/b|n = 1,
where a and b are the semi-axes and n is the exponent.
Special Cases: When n=2, you get an ellipse (or circle if a=b).
When n=1, you get a rhombus. As n→∞, the curve approaches a rectangle.
When 0<n<1, the curve becomes star-shaped (astroid family).
Applications: Superellipses are used in architecture (Sergels Torg in Stockholm),
furniture design (Piet Hein's tables), UI design (iOS app icons use squircles),
and various engineering applications for smooth corner transitions.