Wednesday, April 29, 2009


An interesting mathematical curiosity: the Gömböc (pronounced "gəmbəts"). This is an intriguing object, devised by Hungarian mathematicians Gábor Domokos and Péter Várkonyi, that has the property of self-righting to a single stable position despite being homogeneous, completely convex and not being obviously "flat" or "thin".
As with many other shapes with useful mechanical properties, this self-righting behaviour has already been achieved in nature in animals such as the Indian Star Tortoise. More on this at the Mathematical Intelligencer article Mono-monostatic bodies: the answer to Arnold's question (PDF). The question of whether it is possible to construct a three dimensional body which is mono-monostatic but also homogeneous and convex was raised by the by Russian mathematician Vladimir Arnold. This is of interest because it is known to be impossible in two dimensions.
A gömböc is, incidentally, Hungarian for a round thing, which may apply to dumplings or the sinister pork haggis in the Hungarian folktale A kis gömböc that hangs in a cottage attic and eats a family.

Compare the rattleback or celt, an object of no discernable application, but one also with unusual dynamic properties: in its case, a preferred direction of spin.

Tuesday, April 28, 2009

Russia’s Aqua Star: An Original Underwater scooter

The Aqua Star is an underwater motorcycle that permits the user to go underwater without any special equipment. The way it works is simple. The body of the motorcycle rider stays in the water and the head is encased in a sort of helmet (integrated into the Aqua Star’s body) that serves as a diving bell equipped with an air-supplying system. The controls operate like a bike – just twist the handlebars.
The electronic motor on the Aqua Star permits movement in all directions underwater. The Russian developers of the Aqua Bike came up with several fascinating innovations. For one thing, they used even glass for the helmet instead of the usual spherical glass that distorts the diver’s visibility and makes the eyes get tired.
Developers of the Aqua Star claim their motorcycle can be used at a depth of up to 12 meters (about 42 feet) and ride with 7km/h speed (about 4 miles per hour). The Aqua Star should be ready for market by next summer but the price is still a mystery. The brothers are pushing forward with their newest design, a two-seat motorcycle.