Colossal Gardner, ch. 6


The next Gardner article in the section on plane geometry is on Piet Hein’s superellipse.

Piet Hein was a Danish mathematician, inventor, designer, author, and poet who lived from 1905 to 1996. He created the games Hex, Nimbi, Tower and the Soma Cube. For poetry, he mastered something he called a grook – a short rhyming aphorism. He wrote over 7000 grooks, which have been published in 20 volumes. You can find copies on amazon. I first encountered a book of grooks in the late 1970’s, early 80’s, and I liked them a lot.

Example from the wiki entry:
It may be observed, in a general way,
that life would be better, distinctly
If more of the people with nothing to say
were able to say it succinctly
– Piet Hein

In 1959, the architectural team tasked with rebuilding a congested section of old houses and narrow streets in the heart of Stockholm, Sweden, couldn’t figure out how to do the layout. They approached Piet Hein, who eventually came up with the idea of the superellipse – a curve that fits pleasantly into a rectangle without having the sharper deformations of an ellipse.

The general form of an ellipse is:
abs(x/a)^n + abs(y/b)^n = 1

As n approaches infinity, the shape becomes a rectangle. “a” and “b” are arbitrary constants that represent the semiaxes of the curve, and n is any positive real number.

Piet Hein settled on n = 2.5.

The superellipse has been used as the basis for furniture, park landscaping, and the patterns for Danish postage stamps. When made 3D out of solid brass, referred to as a superegg, it will easily sit on one end without falling over.


Superegg, from the wiki article.

Challenge of the week: Draw your own superellipse and stick it on stuff.

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