The Superegg

Cleaning and Care

The Superegg and the Superellipse it is based on are rather new shapes, yet are two of the most culturally significant and mathematically significant shapes of the 20th century. Due to their appealing and useful design, they have influenced numerous disciplines from industrial design, cartography, plant microscopy, typography, sports stadium design, architecture and computer graphics. The humble 3D Superegg stuns onlookers with its intriguing rolling properties, approachable equation, and its mysterious balancing stability.

Overall, the Superegg and Superellipse are symbols of something much bigger than useful and aesthetic design. They are the result of and represent the synthesis and unification of algebra and geometry. Visit the Math Talk section below for more info.

How Many Times Can you Roll?

The Superegg's origins can be traced back to the early 19th century work of the great French mathematical-physicist and engineer Gabriel Lamé (1795-1870). In 1818, Lamé was studying various closed curves which resemble ellipses (this is a very simplistic synopsis of his curvilinear coordinate system contributions) and published a paper titled Examen de differentes méthodes employées pour résoudre les problèmes de géometrie (Review of different methods used to solve geometry problems). Today, these curves are referred to as Lamé curves and a subset of these curves are called Lamé Ovals or Superellipses. His work in these fields merged algebra and geometry in a way nobody else had. The elegant Superegg would eventually be a serendipitous byproduct of this new body of mathematics.

141 years later in 1959, architects in Stockholm, Sweden were trying to figure out how to direct traffic around an elliptical fountain and within a rectangular plot of land. The city planners turned to Danish Renaissance man Piet Hein (1905-1996). Hein solved the city's problem in under a minute by utilizing Lamé ovals! The specific ratios Hein chose would become known as the famous Superellipse. The intersection Hein designed, Sergels torg, can be seen below.

Piet Hein was known as a popular poet, inventor, designer, polyglot, mathematician, philosopher, artist, author and scientist. He was friends with Nobel Prize winning physicist Niels Bohr, filmmaker Charlie Chaplin, and was known to visit Princeton University to enjoy tea with Albert Einstein. Without Hein, the Superellipse would not have the world-wide cultural appeal it maintains today and would likely be relegated to the mathematical realm. Hein produced Supereggs in various sizes and materials in the 1960s and 1970s. Even John Lennon had a Superegg he would carry in his pocket. Lennon called it the "Alien Egg" and gave it to his friend Uri Geller since it was too weird for him.

Math Talk - θ The Balancing Egg

Piet Hein's Superegg, is a Superellipse rotated on its major axis. Specifically, his Superellipse is such that n=2.5, a=5 and b=6 as indicated in Gabriel Lamé's equation below. Hein chose these parameters since he believed they resulted in the most aesthetically pleasing design. Occasionally though Hein adjusted the major and minor axis ratio +/- a few percent. A Superellipse can be achieved whenever n is greater than 2, however, the exponent 2.5 is what Hein used. This Kickstarter is based on the Superegg, but it would be remiss to not highlight Lamé's equation as much as possible and urge the reader to study its application and unifying nature further in differential geometry and Riemannian geometry.

Design & Precision Machining

Each Superegg is machined from a solid bar of either Copper, Stainless Steel or Titanium. We will NOT be casting them. Below you can see how our Superegg compares to our other shapes in the Solids of Constant Width family. All of the solids in the lineup below are 1.4 in., 45.56 mm wide.