Piet Hein's Squircle

Piet Hein is a fantastic poet-mathematician of little aphorisms he calls "Grooks."  He got me thinking about how mind boggling it is that poetry and mathematics are not taught hand in hand.  What could be more poetic than defining an equation which aptly combines the best qualities of a square and a circle ("squircle")?






Our choicest plans
have fallen through,
our airiest castles
tumbled over,
because of lines
we neatly drew
and later neatly
stumbled over.



Regarding the Squircle, Piet Hein had this to say:

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.

I'll post some more Grooks at a later moment.