Swedish superellipse

Sergels torg, Stockholm, Sweden. Photo via Wikipedia.

The fountain in Sergels torg (English: Sergel’s Square) in Sockholm is in the shape of a “superellipse.” Piet Hein proposed this shape as a practical and aesthetically pleasing compromise between a circle and a rectangle.

What Piet Hein dubbed a superellipse is a curve satisfying

\left| \,\frac{x}{a}\,\right|^{5/2} + \left| \,\frac{y}{b}\,\right|^{5/2} = 1

In the case of Sergels torg, a/b = 6/5. A superellipse is what an analyst would call an Lp ball with p = 2.5 and rescaled axes.

Incidentally, I used curves of this form in a dose-finding method a few years ago. A clinical trial design would pick a, b, and p to match a physician’s desired trade-off between probability of efficacy and probability of toxicity.

Update: A few minutes after I posted this, I realized that there was a bowl on my desk shaped like a superellipse:

The bowl came from Ikea, so there’s another connection to Sweden.

Related post: Volumes of Lp balls

5 thoughts on “Swedish superellipse

  1. Just a nitpick: according to Wikipedia, a superellipse is more general than that: the exponent doesn’t have to be 2.5 (but it still is an L^p ball and rescaled axes, only with p = n). For example, the squircle is a superellipse with n = 4 and a = b.

    off-topic: is math markup parsed in the comments? If so, you could add it to the “You may use these HTML tags and attributes:” text that shows up below the comment box.

  2. If memory serves, a superellipse can be stably stood on any of its four sides.

  3. @Tom Hendrix: Memory does serve: Long ago I turned some super-elllipsoid eggs on a lathe to have fun with the ability to stand them on end.

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