Gabriel Lamé1795–1870
Generalised ellipse
French mathematician whose generalised ellipse equation became the foundation of the superellipse and many smoothly squared forms.
Superellipse
One exponent carries a shape from diamond through circle to near-square. Sweep it across a grid, or nest the whole range inside a single frame.
About this shape
Gabriel Lamé, 1818 · Piet Hein, 1959
The curve is |x/a|ⁿ + |y/b|ⁿ = 1. At n = 1 it is a diamond, at n = 2 an ellipse, and beyond n = 4 it approaches a rounded rectangle, the squircle used for app icons and Piet Hein's Sergels torg. Exponents are interpolated in log space so each step reads as an equal change. Aspect stretches a and b apart.
Behind the mathematics
Piet Hein1905–1996
Superellipse in design
Danish polymath who popularised the superellipse in design and architecture, showing how mathematics can soften the meeting of circle and rectangle.