Two Hungarians puzzled by how certain creatures with shells, like turtles and beetles, are able to self-right have developed a shape with one stable and one unstable point of equilibrium to explain the phenomenon.
“Nature has created such shapes but we did not understand why they are this way,” said Gabor Domokos of the Budapest University of Technology and Economics (BUTE).
“For example if a seed falls it matters which side it lands on, and if I turn a turtle on its back it will care whether it can get back to its feet,” said the head of BUTE’s department of mechanics, materials and structures.
Domokos and a former student, Peter Varkonyi who is now at Princeton University in the United States, took up the challenge and created a shape they named Gomboc which mimics a turtle’s shell.
The shape made front page of the journal Mathematical Intelligencer, echoing the splash made by fellow Hungarian Erno Rubik when he created his cube-shaped puzzle in the 1970s. Domokos and his wife spent hours scouring beaches to collect pebbles as part of a learning process to understand shapes and their mathematical dynamics.
Each pebble was then classified according to how many points of equilibrium each stone had, before the Gomboc was developed. “It is not only about this one shape,” he said.
“We have created a classification system for all other shapes as well.” Domokos said that by shaving off bits of a Gomboc shape it was possible to increase the number of equilibria.
A turtle’s shell is like an imperfect Gomboc, with some curves chopped off it, he said, adding that they were working on a further academic paper which will explore the Gomboc’s implications in more detail.