Mathematicians create a tetrahedron that always lands on the same side

A four -sided form that will always rest on the same side, no matter which side it starts on, has been built by mathematicians, decades after it was only suggested to exist.

Mathematicians have long been fascinated by self -called “monostable” forms that have a preferred resting place when placed on a flat surface. A famous example is Gömböc, a curved, turtle-shell-shaped object that has a precise weight distribution and will rock side aside until it reaches the same stable resting place.

In 1966, the mathematician John Conway worked on how just angular forms balance and proven that a four -sided shape or tetrashedron with an even mass distribution would be impossible. However, he told his colleagues at the time that an unfriendly balanced monostabel Tetrahedron could be possible but not prove it.

Now Gábor Domokos at Budapest University of Technology and Economics, Hungary and his colleagues has built a monostable tetrahedron, which they call Bille, using carbon fiber structures and a plate made of ultra-densen-carbide. The name comes from the Hungarian word for tip, The car.

They first started working on the problem when Domokos asked his student, Gergő Almádi, to search for Conway’s tetrahedron by performing a brute-force search with powerful computers. “You check each tetrahedron, and with a little luck you find it or with time or with [computing power]But a mixture of them, ”says Domokos.

As Conway predicted, they did not find any monostabel Tetrahedra with a smooth weight distribution, but they found some candidate units and continued to prove their existence mathematically.

Domokos and his team then wanted to build a real example, but this turned out to be “an order of magnitude more difficult,” he says. This is because, according to their calculations, the difference between the density of the weight and unweighted parts of the objects needed to be about 5000 times, which means the object should be esteemed by air, but still rigid.

To produce the form, Domocos and his team collaborated with an engineering company and used thousands of euros to precisely construct carbon fiber struts within a tenth of a millimeter and make the tungsten base within a time of a gram.

When Domokos first saw the functioning beetle in real life, he felt he “delivered 1 meter above the group,” he says. “It’s a great pleasure to know that you achieved something that would make John Conway happy.”

“There is no pattern, past example or nothing in nature, which would [have suggested to Conway] That this form exists, “says Domocos.” It was in such an unclear corner of reality that no human [could] Well it “so far” when you have powerful computers and you will pay thousands of dollars “.

The form they built has a specific tilt path between its sides, says Domokos, which tumbles from B to A, from C to A, and from D to C and C to A. There is another kind of monostable tetrahedron that tips sequentilly from d to b to B to a, but domokos who say would need a material that is one-and-one-of that.

Domokos hopes their work will help engineers change the geometry of Lunar Landers to make them less likely to fall over as several recent spacecraft have done. “If you can do it with oven surfaces, you can do it with any other number of faces.”