Piet Hein: the pirate

Mike Frost

21 February 2019

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My day job, in systems and control engineering, takes me to steel-rolling mills around the world. Not so long ago, I was working at the Tata steel plant in Ijmuiden, Holland, and my hotel was the Ijmuiden Holiday Inn. In the summer, this is a wonderful place to stay, with the beach and marina close at hand. I was there in December: it was miserable.

Hex board game. CC BY-SA 3.0

I cheered up a little when I spotted that the hotel conference room was named for Piet Hein. I’m sure that many readers of Chalkdust will know of him. In the early 1940s, Piet Hein invented the game of Hex, in which players take turns to put counters on a hexagonally-tesselated rhomboid board, trying to complete an unbroken line from one side to the other. John Forbes Nash, the game theorist immortalised in A beautiful mind, independently invented a similar game a few years later. Hein also invented the Soma Cube, an elementary but surprisingly difficult dissection of the $3 \times 3 \times 3$ cube, and suggested generalisations of the ellipse and ellipsoid, the superellipse and superegg (see below). Martin Gardner featured “Piet Hein’s superellipse” in his book Mathematical carnival, which was my introduction to Hein.

But Hein was far more than just a recreational mathematician – indeed, he could be described as a renaissance man, such was the breadth of his interests. He was born 16th December 1905 in Copenhagen. He studied at the Institute for theoretical physics, Copenhagen, where Niels Bohr was a colleague and friend. His mathematical game, Tangloids, arose from attempts to visualise the mathematics of Spinors.

Piet had many interests on the art side of the “two-cultures” divide. For example, for decades he wrote aphoristic poems, Grooks, under a pseudonym, for the Danish press. These took on particular significance after the occupation of Denmark during the Second World War. For example, his most famous Grook, the “Consolation Grook”, was both intended and understood as a warning against collaboration with the Nazi occupiers.

Losing one glove
is certainly painful,
but nothing
compared to the pain
of losing one,
throwing away the other,
and finding
the first one again.

If you visit the Piet Hein website, you can buy collections of his Grooks. You can also buy home furnishings based on his designs– for example, superegg lamp stands. His superellipse was adopted for town planning, in which he took an interest; there is a superelliptical roundabout in Stockholm. Hein died on April 17 1996; one of the greatest Danes of the twentieth century.

Sergels Torg, Stockholm. Flickr, CC-BY-SA-2.0

So I was intrigued to know what was in the conference room. Would the deco feature superellipses, Soma cubes or Hex games? Would the lamp stands be supereggs? Would there be Grooks? I went to reception and asked to be let in. The hotel staff eventually realised that I wasn’t going to be easily fobbed off, and acceded to my request.

The conference room wasn’t quite what I expected. The pictures on the walls featured sailboats engaged in naval battles and imposing figures in seventeenth-century garb.

Turns out there’s more than one Piet Hein…

Piet Pieterszoon Hein (1577-1629). Public Domain

The conference room, it turns out, was named in honour of Piet Pieterszoon Hein, a Dutch privateer. He was born in Delft on 25^th November 1577, son of a sea captain. He went to sea young. In his early twenties, he was captured by the Spanish and spent four years as a galley slave – and you thought your job sucked – eventually being released in a prisoner exchange. He became a Captain in the Dutch East India Company, then jumped ships, so to speak, to the Dutch West India Company, where he rose to Admiral of the privateering fleet. In 1624, he briefly took the Brazilian city of Salvador. His most famous achievement, in 1628, was to capture a Spanish Treasure Fleet off Cuba-the spoils paid the wages of the Dutch army for eight months. Sadly, this was to be the highpoint of his life. In a battle off Ostend on 26^th March 1629, a cannonball shattered his shoulder, and he died shortly afterwards.

Here’s the interesting part. Piet Hein the Danish mathematician was a lineal descendant of Piet Hein the Dutch pirate and was named for his illustrious predecessor. Maybe I’m deluded, but I think I can see a family resemblance in their portraits.

First of all: Why can’t I have a pirate for a great, great, great grandfather? Some families have all the luck…

More importantly: On a comprehensive sample of one, the Hein family conclusively prove that the genes which select for piracy also select for recreational mathematics.

So I’d conclude by urging you all to embrace your inner pirate.

Ooh aar Jim lad. Shiver me timbers.

Thank ‘ee kindly.

The superellipse

The superellipse has equation $|x/a|^n+|y/b|^n=1$, where $n$, $a$ and $b$ are positive numbers. The curve was first described by Gabriel Lamé (1795-1870), but Piet Hein realised its aesthetic and practical potential. For $n < 1$, we get what looks like a four-cornered star. For example, $n=1/2$, $a=b=1$ consists of four segments of parabola.

The case $n=1$ gives a parallelogram. For $n=2$, we get an ellipse (a circle when $a=b$):

For $n>2$, the superellipse increasingly approaches a rectangle as $n$ gets larger.

Superellipses with $n>2$ have practical usages. For example, the Aztec Stadium in Mexico City has a superelliptical shape, seen from above.

The Azteca Stadium, Mexico City. Flickr, CC BY-NC-SA 2.0

Hein successfully proposed the Superellipse ($n=2.5$, $a=1.2$, $b=1.0$) as the design for a roundabout in Stockholm, Sergels Torg (shown above). Rotate a superllipse around one of its principal axes, and you get a Superegg. Piet Hein loved this shape, and used it in the design of household fittings such as lampshades.

Piet Hein’s superegg in Egeskov Castle, Denmark. CC BY 2.0

Mike Frost

Mike Frost has degrees in mathematics, astronomy and control engineering. When he’s not doing automation in the steel industry, he moonlights as director of the British Astronomical Association’s historical section. But he still thinks of himself as a mathematician.

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