Math teachers have persistence. Even though knocked off-kilter by a student's off-the-wall question or unexpected teaching moments, the math teachers always seems to right themselves.
That is, math teachers are like the Gömböc. Invented by the Hungarian mathematicians Gábor Domokos and Péter Várkonyi in 2006, the Gömböc is the world's only artificial, self-righting shape (i.e. man-made turtles). Prior to creating it, Domokos and Várkonyi spent a year measuring turtles in the zoo and pet shops in Budapest, digitizing and analyzing their shells...trying to use formal geometry to understand the shapes and functions of a turtle's shell.
You might want to watch a video of the Gömböc in Action (It may make more sense if you understand the language.) As a second video, you might watch Gömböc as Sculptures. A Wikipedia article explains the history and mathematics of Gömböc.
Physically, the Gömböc is unpowered and has a consistent weight throughout. Geometrically, it has "a wide curve on the bottom, surrounded by flat-ish sides and a ridged curve of a top." Theoretically, it is a "mono-monostatic" shape, with one stable point of balance and one unstable point.
As the video shows, when the Gömböc is positioned on the curved portion on its top, it rights itself quickly. But, when placed on its flat side, the righting process takes longer, as the Gömböc rolls back and forward , slows almost to an apparent stop, rolls back and forward quickly, falls onto its stable point of balance, and rights itself.
Gömböcs are not a toy, are expensive (about $1000), and cannot be made in home workshops as its "different angles and proportions have to be measured to within ten microns – one tenth of the thickness of a human hair - to make the shape work." Domokos' new company Gomboc-Shop.com has made the mathematics available...but is it understandable?
Domokos and Várkonyi want to create a polyhedral equivalent, whose surfaces are all flat planes. In turn, they have offered a prize to anyone who creates such a polyhedra: $10,000 divided by the number of planes in the solution. This clever prize removes the known possibility of approximating the curvilinear gömböc with a finite number of planes...estimated to take more than a thousand (leading to a prize of less than $10).
Thanks to MJ (Bellingham) for finding this this weird object and sharing it with me.
Source: Adapted from the website io9.com, a daily publication that covers science, science fiction, and the future