Superellipse
A geometric shape of the general form
(x/a)^n + (y/b)^n = 1
where n >=2 and a and b are the radii of the oval shape.
Though often credited with its invention, Piet Hein did not discover the super-ellipse. The general notation of the form comes from the French mathematician Gabriel Lamé who generalized the equation for the ellipse, describing it as a wider set of curves.
However Hein did popularize the use of the super-ellipse in architecture, urban planning and furniture making, and he DID invent a solid super-egg called a super-ellipsoid based on the super-ellipse with parameters:
(x/4)^2.5 + (y/3)^2.5 = 1
“Man is the animal that draws lines which he himself then stumbles over. In the whole pattern of civilization there have been two tendencies, one toward straight lines and rectangular patterns and one toward circular lines. There are reasons, mechanical and psychological, for both tendencies. Things made with straight lines fit well together and save space. And we can move easily – physically or mentally – around things made with round lines. But we are in a straitjacket, having to accept one or the other, when often some intermediate form would be better. To draw something freehand – such as the patchwork traffic circle they tried in Stockholm – will not do. It isn’t fixed, isn’t definite like a circle or square. You don’t know what it is. It isn’t esthetically satisfying. The super-ellipse solved the problem. It is neither round nor rectangular, but in between. Yet it is fixed, it is definite – it has a unity.” -- Piet Hein
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