In one of his numerous articles on popular mathematics, Martin Gardner related the following anecdote. The piece can be found in his book called The Colossal Book of Mathematics. It originally appeared in the September, 1965 issue of Scientific American which can be accessed online. It concerns Danish scientist, inventor, philosopher and poet Piet Hein’s creation of the superellipse. Gardner said he found the tale in Girolano Benzoni’s book, History of the New World (Venice, 1565). Keep in mind that at the time this happened everyone still believed Columbus had discovered islands in the East Indies. Here’s an English translation of the quote from Benzoni’s book:

“Columbus, being at a party with many noble Spaniards … one of them undertook to say, ‘Mr. Columbus, even if you had not found the Indies, we should not have been devoid of a man who would have attempted the same thing that you did, here in our own country of Spain, as it is full of great men clever in cosmology and literature.’ Columbus said nothing to these words but … placed an egg on the table saying, ‘Gentlemen, I will lay a wager with any of you, that you will not make this egg stand up as I will, naked and without anything at all.’ They all tried and no one succeeded. When the egg came round to the hands of Columbus, by beating it down on the table he fixed it, having thus crushed a little of one end; wherefore all understood what he would have said: That after the deed is done, everybody knows how to do it.”

"Egg" by Kacper "Kangel" Aniolek

"Egg" by Kacper "Kangel"Aniolek
Credit: Wikipedia Commons

That story may or may not be true but Gardner tells of a suspiciously similar tale told fifteen years earlier in Giorgio Vasari’s book, Lives of the Most Eminent Painters, Sculptors and Architects (Florence, 1550). Young Filippo Brunelleschi was one of several architects competing to design a dome for the cathedral of Florence, Santa Maria Del Fiore. His was unusually large and heavy. When City officials asked to see his model he refused to show it. He proposed instead that whoever could make an egg stand upright on a flat piece of marble should be given the contract. So all those masters tried but failed to complete the task. When Brunelleschi’s turn came he made the egg stand by giving a blow on the marble to crush and thus flatten one end. The others protested that they could have done the same thing. Fillippo laughed at them, saying they could also have raised the cupola if they had seen his design.

He was awarded the contract. An ironic ending to this story is that upon completion many years later the dome had the shape of half an egg, flattened at the end.

Brunelleschi's Dome in Florence

Brunelleschi's Dome in Florence
Credit: Charles Herbert Moore via Wikipedia Commons

Of course neither story may be true. It may have taken place years (or centuries) earlier with a completely different cast of characters. After all, eggs have been around for a long time.

But what has the egg to do with Piet Hein? The article was, after all, about an invention of his. (Incidentally, he is always spoken of with both names.) He reflected on the fact that we are surrounded by boxes and circles. Cars are boxes that move on circular wheels down streets that intersect at right angles. We play sports on rectangular courts with spherical balls. Currencies generally come in rectangular paper shapes and round coins. What, he asked himself, is the simplest and most pleasing closed curve that mediates fairly between these two clashing tendencies?

It turned out to be a shape calculated mathematically to lay between an ellipse and a rectangle, which he called a superellipse. Sometimes it's called a "superegg." It has been used in disciplines as diverse as furniture making and city planning. What’s more, a three dimensional superellipse, unlike an egg, will stand on end unaided. The shape closest to it most commonly seen in America is the Safeway grocery logo.

Superellipse sculpture at Egekov Castle in Denmark

Superellipse sculpture at Egeskov Castle in Denmark
Credit: Wikipedia Commons

Piet Hein was famous for little aphoristic poems he called grüks (pronounced grooks). Here are a few:

“A bit beyond perception’s reach, I sometimes believe I see

that life is two locked boxes each containing the other’s key.”


“It ought to be plain how little you gain

by getting excited and vexed.

You’ll always be late for the previous train,

and always on time for the next.”

In this one the “show” is life:

“I’d like to know what this whole show

is all about before it’s out.”

Piet Hein and statue of H.C. Andersen

Piet Hein and H.C. Andersen
Credit: by Andre Savik via Wikipedia Commons

You Must Break Eggs to Make an Omelet --

Or to Discover New Worlds

The three examples above share one theme. While most of us accept nature as it is, some seek to improve it. The colleagues of Columbus and Brunelleschi found the egg’s form adequate as it was. Those two worthies (or whoever the originated the tale) felt it needed reshaping. People generally take round wheels and square basketball courts for granted. Piet Hein dreamed of a more beautiful image.